Theorem imbi1i

Description: Introduce a consequent to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 17-Sep-2013)

	Ref	Expression
Hypothesis	imbi1i.1	|- ( ph <-> ps )
Assertion	imbi1i	|- ( ( ph -> ch ) <-> ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		imbi1i.1	|- ( ph <-> ps )
2		imbi1	|- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )
3	1 2	ax-mp	|- ( ( ph -> ch ) <-> ( ps -> ch ) )