User:Nanobear~enwiki/Generalized modus ponens

Another important inference rule is Generalized modus ponens: for atomic sentences $$p_i, p^{'}_i$$ and $$q$$, where there is a substitution $$\Theta$$ such that $$subst(\Theta, p^{'}_i) = subst(\Theta, p_i)$$, for all $$i$$,


 * $$p^{'}_1, p^{'}_2 ..., p^{'}_n$$ and $$p_1 \land p_2 \land ... \land p_n => q$$

then we can imply $$subst(\Theta, q)$$.

In words: if we have n atomic sentences $$p_i, p^{'}_i$$ and $$q$$ and an implication $$p_1 \land p_2 \land ... \land p_n => q$$ and there is a substitution $$\Theta$$, which, when applied to atomic sentences $$p_i$$ and $$p^{'}_i$$, makes them look identical, then we can infer the result of applying $$\Theta$$ to the conclusion $$q$$.