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Theorem pm4.71r 370
Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120 (with conjunct reversed). (Contributed by NM, 25-Jul-1999.)
Assertion
Ref Expression
pm4.71r ((φψ) ↔ (φ ↔ (ψ φ)))

Proof of Theorem pm4.71r
StepHypRef Expression
1 pm4.71 369 . 2 ((φψ) ↔ (φ ↔ (φ ψ)))
2 ancom 253 . . 3 ((φ ψ) ↔ (ψ φ))
32bibi2i 216 . 2 ((φ ↔ (φ ψ)) ↔ (φ ↔ (ψ φ)))
41, 3bitri 173 1 ((φψ) ↔ (φ ↔ (ψ φ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.71ri  372  pm4.71rd  374
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