Theorem syl12anc

Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009)

	Ref	Expression
Hypotheses	syl12anc.1	|- ( ph -> ps )
	syl12anc.2	|- ( ph -> ch )
	syl12anc.3	|- ( ph -> th )
	syl12anc.4	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
Assertion	syl12anc	|- ( ph -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl12anc.1	|- ( ph -> ps )
2		syl12anc.2	|- ( ph -> ch )
3		syl12anc.3	|- ( ph -> th )
4		syl12anc.4	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
5	2 3	jca	|- ( ph -> ( ch /\ th ) )
6	1 5 4	syl2anc	|- ( ph -> ta )