Theorem syl3anr1

Description: A syllogism inference. (Contributed by NM, 31-Jul-2007)

	Ref	Expression
Hypotheses	syl3anr1.1	|- ( ph -> ps )
	syl3anr1.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
Assertion	syl3anr1	|- ( ( ch /\ ( ph /\ th /\ ta ) ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3anr1.1	|- ( ph -> ps )
2		syl3anr1.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
3	1	3anim1i	|- ( ( ph /\ th /\ ta ) -> ( ps /\ th /\ ta ) )
4	3 2	sylan2	|- ( ( ch /\ ( ph /\ th /\ ta ) ) -> et )