Theorem pm4.71i

Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 4-Jan-2004)

	Ref	Expression
Hypothesis	pm4.71i.1	|- ( ph -> ps )
Assertion	pm4.71i	|- ( ph <-> ( ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.71i.1	|- ( ph -> ps )
2		pm4.71	|- ( ( ph -> ps ) <-> ( ph <-> ( ph /\ ps ) ) )
3	1 2	mpbi	|- ( ph <-> ( ph /\ ps ) )