Theorem syl5ib

Description: A mixed syllogism inference. (Contributed by NM, 12-Jan-1993)

	Ref	Expression
Hypotheses	syl5ib.1	|- ( ph -> ps )
	syl5ib.2	|- ( ch -> ( ps <-> th ) )
Assertion	syl5ib	|- ( ch -> ( ph -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	|- ( ph -> ps )
2		syl5ib.2	|- ( ch -> ( ps <-> th ) )
3	2	biimpd	|- ( ch -> ( ps -> th ) )
4	1 3	syl5	|- ( ch -> ( ph -> th ) )