Strong points of the material implication
The material implication is truth-functional
? A connective * is truth-functional if the truth value of sentences of the form p*q is determined by the truth values of p and q.
The material implication validates the deduction theorem
? A conditional ? validates the deduction theorem if the following holds:
p ? q if and only if ? p ? q
? The deduction theorem implies that proofs and (instances of) rules of inference correspond to provable conditional sentences.