Theorem pm5.74ri

Description: Distribution of implication over biconditional (reverse inference form). (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypothesis	pm5.74ri.1	|- ( ( ph -> ps ) <-> ( ph -> ch ) )
Assertion	pm5.74ri	|- ( ph -> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.74ri.1	|- ( ( ph -> ps ) <-> ( ph -> ch ) )
2		pm5.74	|- ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3	1 2	mpbir	|- ( ph -> ( ps <-> ch ) )