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Theorem pm4.71r 664
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 pm4.71 663 . 2 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜑𝜓)))
2 ancom 465 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
32bibi2i 326 . 2 ((𝜑 ↔ (𝜑𝜓)) ↔ (𝜑 ↔ (𝜓𝜑)))
41, 3bitri 264 1 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 385
This theorem is referenced by:  pm4.71ri  666  pm4.71rd  668
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