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Theorem syl332anc 1259
Description: Syllogism combined with contraction. (Contributed by NM, 11-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 )
syl332anc.9  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et  /\  ze )  /\  ( si  /\  rh ) )  ->  mu )
Assertion
Ref Expression
syl332anc  |-  ( ph  ->  mu )

Proof of Theorem syl332anc
StepHypRef 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 )
97, 8jca 532 . 2  |-  ( ph  ->  ( si  /\  rh ) )
10 syl332anc.9 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et  /\  ze )  /\  ( si  /\  rh ) )  ->  mu )
111, 2, 3, 4, 5, 6, 9, 10syl331anc 1253 1  |-  ( ph  ->  mu )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 973
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 185  df-an 371  df-3an 975
This theorem is referenced by:  mdetunilem5  18987  mdetuni0  18992  lnjatN  34977  lncmp  34980  cdlema1N  34988  4atexlemex6  35271  cdlemd4  35398  cdleme18c  35490  cdleme18d  35492  cdleme19b  35501  cdleme21ct  35526  cdleme21d  35527  cdleme21e  35528  cdleme21k  35535  cdleme22g  35545  cdleme24  35549  cdleme27a  35564  cdleme27N  35566  cdleme28a  35567  cdleme40n  35665  cdlemg16zz  35857  cdlemg37  35886  cdlemk21-2N  36088  cdlemk20-2N  36089  cdlemk28-3  36105  cdlemk19xlem  36139
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