Theorem pm4.71r 636

Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120 (with conjunct reversed).

Assertion

Ref	Expression
pm4.71r	|- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Proof of Theorem pm4.71r

Step	Hyp	Ref	Expression
1		pm4.71 635	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2		ancom 435	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
3	2	bibi2i 608	. 2 |- ((ph <-> (ph /\ ps)) <-> (ph <-> (ps /\ ph)))
4	1, 3	bitr 173	1 |- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  pm4.71ri 638  pm4.71rd 639  bimsc1 750

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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