This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm4.71rd

Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 10-Feb-2005)

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

Proof

Step	Hyp	Ref	Expression
1		pm4.71rd.1	\|- ( ph -> ( ps -> ch ) )
2	1	pm4.71d	\|- ( ph -> ( ps <-> ( ps /\ ch ) ) )
3	2	biancomd	\|- ( ph -> ( ps <-> ( ch /\ ps ) ) )