Theorem syl3an3

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995) (Proof shortened by Wolf Lammen, 26-Jun-2022)

	Ref	Expression
Hypotheses	syl3an3.1	|- ( ph -> th )
	syl3an3.2	|- ( ( ps /\ ch /\ th ) -> ta )
Assertion	syl3an3	|- ( ( ps /\ ch /\ ph ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl3an3.1	|- ( ph -> th )
2		syl3an3.2	|- ( ( ps /\ ch /\ th ) -> ta )
3	1	3anim3i	|- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch /\ th ) )
4	3 2	syl	|- ( ( ps /\ ch /\ ph ) -> ta )