Theorem syld3an1

Description: A syllogism inference. (Contributed by NM, 7-Jul-2008) (Proof shortened by Wolf Lammen, 26-Jun-2022)

	Ref	Expression
Hypotheses	syld3an1.1	|- ( ( ch /\ ps /\ th ) -> ph )
	syld3an1.2	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	syld3an1	|- ( ( ch /\ ps /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syld3an1.1	|- ( ( ch /\ ps /\ th ) -> ph )
2		syld3an1.2	|- ( ( ph /\ ps /\ th ) -> ta )
3		simp2	|- ( ( ch /\ ps /\ th ) -> ps )
4		simp3	|- ( ( ch /\ ps /\ th ) -> th )
5	1 3 4 2	syl3anc	|- ( ( ch /\ ps /\ th ) -> ta )