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Theorem syl321anc 1204
Description: Syllogism combined with contraction. (Contributed by NM, 11-Jul-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 )
syl321anc.7  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et )  /\  ze )  ->  si )
Assertion
Ref Expression
syl321anc  |-  ( ph  ->  si )

Proof of Theorem syl321anc
StepHypRef Expression
1 sylXanc.1 . 2  |-  ( ph  ->  ps )
2 sylXanc.2 . 2  |-  ( ph  ->  ch )
3 sylXanc.3 . 2  |-  ( ph  ->  th )
4 sylXanc.4 . . 3  |-  ( ph  ->  ta )
5 sylXanc.5 . . 3  |-  ( ph  ->  et )
64, 5jca 518 . 2  |-  ( ph  ->  ( ta  /\  et ) )
7 sylXanc.6 . 2  |-  ( ph  ->  ze )
8 syl321anc.7 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et )  /\  ze )  ->  si )
91, 2, 3, 6, 7, 8syl311anc 1196 1  |-  ( ph  ->  si )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  syl322anc  1210  cxple2ad  20072  chordthmlem3  20131  islimrs4  25582  4noncolr2  29643  4noncolr1  29644  3atlem5  29676  2lplnj  29809  llnmod2i2  30052  dalawlem11  30070  dalawlem12  30071  cdleme43dN  30681  cdleme4gfv  30696  cdlemeg46nlpq  30706  cdlemg17bq  30862  cdlemg31b0N  30883  cdlemg31b0a  30884  cdlemg31c  30888  cdlemg39  30905  cdlemk47  31138
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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