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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  30301  cdleme16b  31013  cdleme18d  31029  cdleme19d  31040  cdleme20bN  31044  cdleme20l1  31054  cdleme22cN  31076  cdleme22eALTN  31079  cdleme22f  31080  cdlemg33c0  31436  cdlemk5  31570  cdlemk5u  31595  cdlemky  31660  cdlemkyyN  31696
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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