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Theorem syl233anc 1213
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 519 . 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 1207 1  |-  ( ph  ->  mu )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  2llnjN  30364  cdleme16b  31076  cdleme18d  31092  cdleme19d  31103  cdleme20bN  31107  cdleme20l1  31117  cdleme22cN  31139  cdleme22eALTN  31142  cdleme22f  31143  cdlemg33c0  31499  cdlemk5  31633  cdlemk5u  31658  cdlemky  31723  cdlemkyyN  31759
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 178  df-an 361  df-3an 938
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