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Theorem syl332anc 1250
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 1244 1  |-  ( ph  ->  mu )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965
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 967
This theorem is referenced by:  mdetunilem5  18557  mdetuni0  18562  lnjatN  33782  lncmp  33785  cdlema1N  33793  4atexlemex6  34076  cdlemd4  34203  cdleme18c  34295  cdleme18d  34297  cdleme19b  34306  cdleme21ct  34331  cdleme21d  34332  cdleme21e  34333  cdleme21k  34340  cdleme22g  34350  cdleme24  34354  cdleme27a  34369  cdleme27N  34371  cdleme28a  34372  cdleme40n  34470  cdlemg16zz  34662  cdlemg37  34691  cdlemk21-2N  34893  cdlemk20-2N  34894  cdlemk28-3  34910  cdlemk19xlem  34944
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