Theorem impbid2

Description: Infer an equivalence from two implications. (Contributed by NM, 6-Mar-2007) (Proof shortened by Wolf Lammen, 27-Sep-2013)

	Ref	Expression
Hypotheses	impbid2.1	|- ( ps -> ch )
	impbid2.2	|- ( ph -> ( ch -> ps ) )
Assertion	impbid2	|- ( ph -> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		impbid2.1	|- ( ps -> ch )
2		impbid2.2	|- ( ph -> ( ch -> ps ) )
3	2 1	impbid1	|- ( ph -> ( ch <-> ps ) )
4	3	bicomd	|- ( ph -> ( ps <-> ch ) )