user8509: London System is an opening for white, that goes d4, Bf4, e3, Nf3, Nd2, c3. The move order generally doesn't matter too much and there are lots of ways to transpose into this.
However, what I want to know now, is the horizontally mirrored way also a valid system? White will play e4, Bc4, d3, Nc3, Ne2, f3.
(Note this is not the same as the Italian Game because there, the g Knight goes to f3 instead of e2.)
So is this a real system, and if so, what is its name? I'd like to read more about it and its theory. Is it sound? Are there way more traps white has to watch out for?

user20721: Unaware of any special name given to that full sequence of moves, especially as a 'system' as opposed to an opening variation name.
f3 is a major mistake and would not be played except by beginners. there is a difference between qp and kp setups so that they cannot be mirrored well like  you asked. 
Some of the previous move sequences do have a name.  It would roughly fit in the bishops opening or some others depending on what black did. 
I found some  games of 2500+ players using those moves up to f3 which is terrible bad and white won 3 of the ones I tracked in detail  based on most likely moves according to one tablebase. 
Which I suspect is that winning is more because of the unusualness than the soundness.  The position at that point is dead even and any winning came much later from other moves.
The opening is unusual but playable although apparently not at the GM level for black which further reinforces my belief that the value comes from what happens later and depends how both sides play.

user19877: The answer is no since f3 would never be played there by any strong player as it is weakening, but has no compensating advantages.
That is very close to some virtually-impossible-to-get-to lines in the Bishop's Opening/Vienna game since unlike the queen-pawn London, black has many more ways to throw a wrench into the attempt to play moves without thinking. In an idea world where black cooperates, in the Bishops's, white can try to play for that setup, but would  play f4, which has the advantage of attacking the black center, and opening the f-file.
You can see from this contrived variation that black has many better options, and is not likely to just submit to white's desire to play a London on the kingside. In no case would f3 be good.
  [FEN ""]

 1. e4 e5 2. Bc4 Nf6 3. d3 Nc6 4. Nc3 Be7 (4... Na5 $1 {Blows up the whole idea. }) (4... Bc5 $1 5. Nge2 d6 6. O-O a6 7. Kh1 $2 Ng4 {So it is impossible to get in f4 here.}) 5. Nge2 d6 6. O-O (6. a3 $1) 6... O-O 7. f4 (7. a3 $1) 

.
 [fen "rnbqkbnr/pppppppp/8/8/2B1P3/2NP1P2/PPP1N1PP/R1BQK2R w KQ - 0 1"]

.

8509: <p>London System is an opening for white, that goes d4, Bf4, e3, Nf3, Nd2, c3. The move order generally doesn't matter too much and there are lots of ways to transpose into this.</p>

<p>However, what I want to know now, <strong>is the horizontally mirrored way also a valid system?</strong> White will play e4, Bc4, d3, Nc3, Ne2, f3.</p>

<p>(Note this is not the same as the Italian Game because there, the g Knight goes to f3 instead of e2.)</p>

<p>So is this a real system, and if so, what is its name? I'd like to read more about it and its theory. Is it sound? Are there way more traps white has to watch out for?</p>
 20721: <p>Unaware of any special name given to that full sequence of moves, especially as a 'system' as opposed to an opening variation name.</p>

<p>f3 is a major mistake and would not be played except by beginners. there is a difference between qp and kp setups so that they cannot be mirrored well like  you asked. </p>

<p>Some of the previous move sequences do have a name.  It would roughly fit in the bishops opening or some others depending on what black did. </p>

<p>I found some  games of 2500+ players using those moves up to f3 which is terrible bad and white won 3 of the ones I tracked in detail  based on most likely moves according to one tablebase. </p>

<p>Which I suspect is that winning is more because of the unusualness than the soundness.  The position at that point is dead even and any winning came much later from other moves.</p>

<p>The opening is unusual but playable although apparently not at the GM level for black which further reinforces my belief that the value comes from what happens later and depends how both sides play.</p>
 19877: <p>The answer is no since f3 would never be played there by any strong player as it is weakening, but has no compensating advantages.</p>

<p>That is very close to some virtually-impossible-to-get-to lines in the Bishop's Opening/Vienna game since unlike the queen-pawn London, black has many more ways to throw a wrench into the attempt to play moves without thinking. In an idea world where black cooperates, in the Bishops's, white can try to play for that setup, but would  play f4, which has the advantage of attacking the black center, and opening the f-file.</p>

<p>You can see from this contrived variation that black has many better options, and is not likely to just submit to white's desire to play a London on the kingside. In no case would f3 be good.</p>

<pre><code>  [FEN ""]

 1. e4 e5 2. Bc4 Nf6 3. d3 Nc6 4. Nc3 Be7 (4... Na5 $1 {Blows up the whole idea. }) (4... Bc5 $1 5. Nge2 d6 6. O-O a6 7. Kh1 $2 Ng4 {So it is impossible to get in f4 here.}) 5. Nge2 d6 6. O-O (6. a3 $1) 6... O-O 7. f4 (7. a3 $1) 
</code></pre>

<p>.</p>

<pre><code> [fen "rnbqkbnr/pppppppp/8/8/2B1P3/2NP1P2/PPP1N1PP/R1BQK2R w KQ - 0 1"]
</code></pre>

<p>.</p>
