Theorem syl333anc

Description: A syllogism inference combined with contraction. (Contributed by NM, 10-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 )
	syl333anc.9	|- ( ph -> mu )
	syl333anc.10	|- ( ( ( ps /\ ch /\ th ) /\ ( ta /\ et /\ ze ) /\ ( si /\ rh /\ mu ) ) -> la )
Assertion	syl333anc	|- ( ph -> la )

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		syl333anc.9	|- ( ph -> mu )
10		syl333anc.10	|- ( ( ( ps /\ ch /\ th ) /\ ( ta /\ et /\ ze ) /\ ( si /\ rh /\ mu ) ) -> la )
11	7 8 9	3jca	|- ( ph -> ( si /\ rh /\ mu ) )
12	1 2 3 4 5 6 11 10	syl331anc	|- ( ph -> la )