<p>There is a converse, an <a href="https://en.wikipedia.org/wiki/Implicant" rel="nofollow noreferrer">implicant</a>. In that case if the implicant is true, the whole expression must be true.</p>
<p>From a search, it seems the one you want is an <strong>implicate</strong>. See e.g. <a href="http://www.cs.albany.edu/%7Eritries/KAIS-1819R1.pdf" rel="nofollow noreferrer">http://www.cs.albany.edu/~ritries/KAIS-1819R1.pdf</a> or <a href="https://arxiv.org/ftp/arxiv/papers/1401/1401.3475.pdf" rel="nofollow noreferrer">https://arxiv.org/ftp/arxiv/papers/1401/1401.3475.pdf</a>. Since you mention &quot;variable/term&quot;, an implicate must be a literal (a variable or a negation of a variable) or a disjunction of literals.</p>
<p>But it seems to be even less known than implicant and easily confused with the verb.</p>
In predicate logic, is there a word for a term that must be true in all cases for the expression to be true?
<p>Take the following example:</p>
<pre><code>A AND (B OR C)
</code></pre>
<p>Obviously <em>A</em> must be true for the expression to be true.</p>
<p>Another example:</p>
<pre><code>(A AND (B OR C)) OR (D AND E AND A)
</code></pre>
<p>Again, <em>A</em> has to be true, but appears multiple times, in two different legs of the expression.</p>
<p>Is there a word for a variable/term that <em>must</em> be true regardless of how deeply nested it is for the expression as a whole to be true? Something like a dominant node in graph theory.</p>