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Metamath Proof Explorer

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 ) )