Syntax Definition wi 3

Description: If ph and ps are wff's, so is (ph -> ps) or "ph implies ps." Part of the recursive definition of a wff. The resulting wff is (interpreted as) false when ph is true and ps is false; it is true otherwise. (Think of the truth table for an OR gate with input ph connected through an inverter.) The left-hand wff is called the antecedent, and the right-hand wff is called the consequent. In the case of (ph -> (ps -> ch)), the middle ps may be informally called either an antecedent or part of the consequent depending on context.

Hypotheses

Ref	Expression
wph	wff ph
wps	wff ps

Assertion

Ref	Expression
wi	wff (ph -> ps)

This syntax is primitive. The first axiom using it is ax-1 4.

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