Logical implication is an operation on two logical propositions. If p and q are two logical propositions, (p → q), pronounced "p implies q" or "if p then q" is a logical proposition that is true if p is false, or if both p and q are true. The proposition (p → q) is logically equivalent to the proposition ((!p) | q). In the conditional p → q, the antecedent is p and the consequent is q.