Theorem syl3anl2

Description: A syllogism inference. (Contributed by NM, 24-Feb-2005) (Proof shortened by Wolf Lammen, 27-Jun-2022)

	Ref	Expression
Hypotheses	syl3anl2.1	|- ( ph -> ch )
	syl3anl2.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
Assertion	syl3anl2	|- ( ( ( ps /\ ph /\ th ) /\ ta ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3anl2.1	|- ( ph -> ch )
2		syl3anl2.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
3	1	3anim2i	|- ( ( ps /\ ph /\ th ) -> ( ps /\ ch /\ th ) )
4	3 2	sylan	|- ( ( ( ps /\ ph /\ th ) /\ ta ) -> et )