Substitution
There is a general procedure, the substitution rule, that allows additional tautologies to be constructed from a given tautology (Kleene 1967 sec. 3). Suppose that S is a tautology and for each propositional variable A in S a fixed sentence SA is chosen. Then the sentence obtained by replacing each variable A in S with the corresponding sentence SA is also a tautology.
For example, let S be, a tautology. Let SA be and let SB be . It follows from the substitution rule that the sentence
is a tautology.
Read more about this topic: Tautology (logic)
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