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Theorem syl212anc 1236
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 )
syl212anc.6  |-  ( ( ( ps  /\  ch )  /\  th  /\  ( ta  /\  et ) )  ->  ze )
Assertion
Ref Expression
syl212anc  |-  ( ph  ->  ze )

Proof of Theorem syl212anc
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 530 . 2  |-  ( ph  ->  ( ta  /\  et ) )
7 syl212anc.6 . 2  |-  ( ( ( ps  /\  ch )  /\  th  /\  ( ta  /\  et ) )  ->  ze )
81, 2, 3, 6, 7syl211anc 1232 1  |-  ( ph  ->  ze )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    /\ w3a 971
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 369  df-3an 973
This theorem is referenced by:  rmob  3416  pntrmax  23950  tglineineq  24227  tglineinteq  24229  paddasslem4  35963  4atexlemu  36204  4atexlemv  36205  cdleme20aN  36451  cdleme20g  36457  cdlemg9a  36774  cdlemg12a  36785  cdlemg17dALTN  36806  cdlemg18b  36821  cdlemg18c  36822
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