Theorem syld3an2

Description: A syllogism inference. (Contributed by NM, 20-May-2007)

	Ref	Expression
Hypotheses	syld3an2.1	|- ( ( ph /\ ch /\ th ) -> ps )
	syld3an2.2	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	syld3an2	|- ( ( ph /\ ch /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syld3an2.1	|- ( ( ph /\ ch /\ th ) -> ps )
2		syld3an2.2	|- ( ( ph /\ ps /\ th ) -> ta )
3		simp1	|- ( ( ph /\ ch /\ th ) -> ph )
4		simp3	|- ( ( ph /\ ch /\ th ) -> th )
5	3 1 4 2	syl3anc	|- ( ( ph /\ ch /\ th ) -> ta )