Theorem syl3anr2

Description: A syllogism inference. (Contributed by NM, 1-Aug-2007) (Proof shortened by Wolf Lammen, 27-Jun-2022)

	Ref	Expression
Hypotheses	syl3anr2.1	|- ( ph -> th )
	syl3anr2.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
Assertion	syl3anr2	|- ( ( ch /\ ( ps /\ ph /\ ta ) ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3anr2.1	|- ( ph -> th )
2		syl3anr2.2	|- ( ( ch /\ ( ps /\ th /\ ta ) ) -> et )
3	1	3anim2i	|- ( ( ps /\ ph /\ ta ) -> ( ps /\ th /\ ta ) )
4	3 2	sylan2	|- ( ( ch /\ ( ps /\ ph /\ ta ) ) -> et )