Theorem pm4.71r 612

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	|- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Proof of Theorem pm4.71r

Step	Hyp	Ref	Expression
1		pm4.71 611	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2		ancom 437	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
3	2	bibi2i 304	. 2 |- ((ph <-> (ph /\ ps)) <-> (ph <-> (ps /\ ph)))
4	1, 3	bitri 240	1 |- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  pm4.71ri  614  pm4.71rd  616