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Theorem syl212anc 1229
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 532 . 2  |-  ( ph  ->  ( ta  /\  et ) )
7 syl212anc.6 . 2  |-  ( ( ( ps  /\  ch )  /\  th  /\  ( ta  /\  et ) )  ->  ze )
81, 2, 3, 6, 7syl211anc 1225 1  |-  ( ph  ->  ze )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965
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 371  df-3an 967
This theorem is referenced by:  rmob  3394  pntrmax  22947  paddasslem4  33806  4atexlemu  34047  4atexlemv  34048  cdleme20aN  34292  cdleme20g  34298  cdlemg9a  34615  cdlemg12a  34626  cdlemg17dALTN  34647  cdlemg18b  34662  cdlemg18c  34663
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