Theorem pm4.71r

Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of WhiteheadRussell p. 120 (with conjunct reversed). (Contributed by NM, 25-Jul-1999)

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

Proof

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