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Theorem syl233anc 1211
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 )
syl233anc.9  |-  ( ( ( ps  /\  ch )  /\  ( th  /\  ta  /\  et )  /\  ( ze  /\  si  /\  rh ) )  ->  mu )
Assertion
Ref Expression
syl233anc  |-  ( ph  ->  mu )

Proof of Theorem syl233anc
StepHypRef Expression
1 sylXanc.1 . . 3  |-  ( ph  ->  ps )
2 sylXanc.2 . . 3  |-  ( ph  ->  ch )
31, 2jca 518 . 2  |-  ( ph  ->  ( ps  /\  ch ) )
4 sylXanc.3 . 2  |-  ( ph  ->  th )
5 sylXanc.4 . 2  |-  ( ph  ->  ta )
6 sylXanc.5 . 2  |-  ( ph  ->  et )
7 sylXanc.6 . 2  |-  ( ph  ->  ze )
8 sylXanc.7 . 2  |-  ( ph  ->  si )
9 sylXanc.8 . 2  |-  ( ph  ->  rh )
10 syl233anc.9 . 2  |-  ( ( ( ps  /\  ch )  /\  ( th  /\  ta  /\  et )  /\  ( ze  /\  si  /\  rh ) )  ->  mu )
113, 4, 5, 6, 7, 8, 9, 10syl133anc 1205 1  |-  ( ph  ->  mu )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  2llnjN  29035  cdleme16b  29747  cdleme18d  29763  cdleme19d  29774  cdleme20bN  29778  cdleme20l1  29788  cdleme22cN  29810  cdleme22eALTN  29813  cdleme22f  29814  cdlemg33c0  30170  cdlemk5  30304  cdlemk5u  30329  cdlemky  30394  cdlemkyyN  30430
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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