If the negation of "p" were provable, then Bew(G("p")) would be provable (because "p" was constructed to be equivalent to the negation of Bew(G("p"))). However, for each specific number "x", "x" cannot be the Gödel number of the proof of "p", because "p" is not provable (from the previous paragraph). Thus on one hand the system proves there is a number with a certain property (that it is the Gödel number of the proof of "p"), but on the other hand, for every specific number "x", we can prove that it does not have this property. This is impossible in an ω-consistent system. Thus the negation of "p" is not provable.