Theorem syl3anr3

Description: A syllogism inference. (Contributed by NM, 23-Aug-2007)

	Ref	Expression
Hypotheses	syl3anr3.1	|- ( ph -> ta )
	syl3anr3.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
Assertion	syl3anr3	|- ( ( ch /\ ( ps /\ th /\ ph ) ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3anr3.1	|- ( ph -> ta )
2		syl3anr3.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
3	1	3anim3i	|- ( ( ps /\ th /\ ph ) -> ( ps /\ th /\ ta ) )
4	3 2	sylan2	|- ( ( ch /\ ( ps /\ th /\ ph ) ) -> et )