Theorem sylan2i

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypotheses	sylan2i.1	|- ( ph -> th )
	sylan2i.2	|- ( ps -> ( ( ch /\ th ) -> ta ) )
Assertion	sylan2i	|- ( ps -> ( ( ch /\ ph ) -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan2i.1	|- ( ph -> th )
2		sylan2i.2	|- ( ps -> ( ( ch /\ th ) -> ta ) )
3	1	a1i	|- ( ps -> ( ph -> th ) )
4	3 2	sylan2d	|- ( ps -> ( ( ch /\ ph ) -> ta ) )