Theorem impbida

Description: Deduce an equivalence from two implications. Variant of impbid . (Contributed by NM, 17-Feb-2007)

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

Proof

Step	Hyp	Ref	Expression
1		impbida.1	|- ( ( ph /\ ps ) -> ch )
2		impbida.2	|- ( ( ph /\ ch ) -> ps )
3	1	ex	|- ( ph -> ( ps -> ch ) )
4	2	ex	|- ( ph -> ( ch -> ps ) )
5	3 4	impbid	|- ( ph -> ( ps <-> ch ) )