Theorem syld3an3

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

	Ref	Expression
Hypotheses	syld3an3.1	|- ( ( ph /\ ps /\ ch ) -> th )
	syld3an3.2	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	syld3an3	|- ( ( ph /\ ps /\ ch ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syld3an3.1	|- ( ( ph /\ ps /\ ch ) -> th )
2		syld3an3.2	|- ( ( ph /\ ps /\ th ) -> ta )
3		simp1	|- ( ( ph /\ ps /\ ch ) -> ph )
4		simp2	|- ( ( ph /\ ps /\ ch ) -> ps )
5	3 4 1 2	syl3anc	|- ( ( ph /\ ps /\ ch ) -> ta )