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Theorem pm4.71r 376
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 ↔ (𝜓𝜑)))

Proof of Theorem pm4.71r
StepHypRef Expression
1 pm4.71 375 . 2 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜑𝜓)))
2 ancom 257 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
32bibi2i 220 . 2 ((𝜑 ↔ (𝜑𝜓)) ↔ (𝜑 ↔ (𝜓𝜑)))
41, 3bitri 177 1 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  pm4.71ri  378  pm4.71rd  380
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