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Syntax Definition wi 4
Description: If φ and ψ are wff's, so is (φψ) or "φ implies ψ." Part of the recursive definition of a wff. The resulting wff is (interpreted as) false when φ is true and ψ is false; it is true otherwise. (Think of the truth table for an OR gate with input φ 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 (φ → (ψχ)), the middle ψ may be informally called either an antecedent or part of the consequent depending on context.
Hypotheses
Ref Expression
wph wff φ
wps wff ψ
Assertion
Ref Expression
wi wff (φψ)

This syntax is primitive. The first axiom using it is ax-1 5.

Colors of variables: wff set class
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