MAT309H1 Lecture Notes - Lecture 13: If And Only If
Document Summary
T is substitutable for in : q1, q2: Rules of inference < , : pc. If is tautology, < , > must be rule of inference. If = , then we need p to be a tautology: qr: is not free in , and let be a formula. We need to check that is a tautology make a truth table. Pick a variable y not occurring in . Ex: the term is substitutable for in (q1) (pc) Corollary let be a set of nonlogical axioms and " obtained by adding or deleting universal quantifiers that have scope the whole formula to each element from then iff " . Remark: we may consider the set of nonlogical axioms to consist of sentences. This is a deduction of from then. Proof: fix this and we know that. Using known theorem, it suffices to show that: C r. of in. s. t then c. C for every we show that (pc)
