Theorem syl3anl3

Description: A syllogism inference. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypotheses	syl3anl3.1	|- ( ph -> th )
	syl3anl3.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
Assertion	syl3anl3	|- ( ( ( ps /\ ch /\ ph ) /\ ta ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3anl3.1	|- ( ph -> th )
2		syl3anl3.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
3	1	3anim3i	|- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch /\ th ) )
4	3 2	sylan	|- ( ( ( ps /\ ch /\ ph ) /\ ta ) -> et )