Theorem impbid1

Description: Infer an equivalence from two implications. (Contributed by NM, 6-Mar-2007)

	Ref	Expression
Hypotheses	impbid1.1	|- ( ph -> ( ps -> ch ) )
	impbid1.2	|- ( ch -> ps )
Assertion	impbid1	|- ( ph -> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		impbid1.1	|- ( ph -> ( ps -> ch ) )
2		impbid1.2	|- ( ch -> ps )
3	2	a1i	|- ( ph -> ( ch -> ps ) )
4	1 3	impbid	|- ( ph -> ( ps <-> ch ) )