Theorem syl323anc

Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012)

	Ref	Expression
Hypotheses	syl3anc.1	|- ( ph -> ps )
	syl3anc.2	|- ( ph -> ch )
	syl3anc.3	|- ( ph -> th )
	syl3Xanc.4	|- ( ph -> ta )
	syl23anc.5	|- ( ph -> et )
	syl33anc.6	|- ( ph -> ze )
	syl133anc.7	|- ( ph -> si )
	syl233anc.8	|- ( ph -> rh )
	syl323anc.9	|- ( ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) /\ ( ze /\ si /\ rh ) ) -> mu )
Assertion	syl323anc	|- ( ph -> mu )

Proof

Step	Hyp	Ref	Expression
1		syl3anc.1	|- ( ph -> ps )
2		syl3anc.2	|- ( ph -> ch )
3		syl3anc.3	|- ( ph -> th )
4		syl3Xanc.4	|- ( ph -> ta )
5		syl23anc.5	|- ( ph -> et )
6		syl33anc.6	|- ( ph -> ze )
7		syl133anc.7	|- ( ph -> si )
8		syl233anc.8	|- ( ph -> rh )
9		syl323anc.9	|- ( ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) /\ ( ze /\ si /\ rh ) ) -> mu )
10	4 5	jca	|- ( ph -> ( ta /\ et ) )
11	1 2 3 10 6 7 8 9	syl313anc	|- ( ph -> mu )