Theorem syl333anc 1214

Description: A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)

Hypotheses

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

Assertion

Ref	Expression
syl333anc	|- (ph -> la)

Proof of Theorem syl333anc

Step	Hyp	Ref	Expression
1		sylXanc.1	. 2 |- (ph -> ps)
2		sylXanc.2	. 2 |- (ph -> ch)
3		sylXanc.3	. 2 |- (ph -> th)
4		sylXanc.4	. 2 |- (ph -> ta)
5		sylXanc.5	. 2 |- (ph -> et)
6		sylXanc.6	. 2 |- (ph -> ze)
7		sylXanc.7	. . 3 |- (ph -> si)
8		sylXanc.8	. . 3 |- (ph -> rh)
9		sylXanc.9	. . 3 |- (ph -> mu)
10	7, 8, 9	3jca 1132	. 2 |- (ph -> (si /\ rh /\ mu))
11		syl333anc.10	. 2 |- (((ps /\ ch /\ th) /\ (ta /\ et /\ ze) /\ (si /\ rh /\ mu)) -> la)
12	1, 2, 3, 4, 5, 6, 10, 11	syl331anc 1207	1 |- (ph -> la)

Syntax hints:   -> wi 4   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)