Theorem biimpcd

Description: Deduce a commuted implication from a logical equivalence. (Contributed by NM, 3-May-1994) (Proof shortened by Wolf Lammen, 22-Sep-2013)

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

Proof

Step	Hyp	Ref	Expression
1		biimpcd.1	|- ( ph -> ( ps <-> ch ) )
2		id	|- ( ps -> ps )
3	2 1	syl5ibcom	|- ( ps -> ( ph -> ch ) )