Theorem syl5ibrcom

Description: A mixed syllogism inference. (Contributed by NM, 20-Jun-2007)

	Ref	Expression
Hypotheses	syl5ibr.1	|- ( ph -> th )
	syl5ibr.2	|- ( ch -> ( ps <-> th ) )
Assertion	syl5ibrcom	|- ( ph -> ( ch -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ibr.1	|- ( ph -> th )
2		syl5ibr.2	|- ( ch -> ( ps <-> th ) )
3	1 2	syl5ibr	|- ( ch -> ( ph -> ps ) )
4	3	com12	|- ( ph -> ( ch -> ps ) )