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Theorem syl323anc 1249
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 )
syl323anc.9  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et )  /\  ( ze  /\  si  /\  rh ) )  ->  mu )
Assertion
Ref Expression
syl323anc  |-  ( ph  ->  mu )

Proof of Theorem syl323anc
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 sylXanc.6 . 2  |-  ( ph  ->  ze )
8 sylXanc.7 . 2  |-  ( ph  ->  si )
9 sylXanc.8 . 2  |-  ( ph  ->  rh )
10 syl323anc.9 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et )  /\  ( ze  /\  si  /\  rh ) )  ->  mu )
111, 2, 3, 6, 7, 8, 9, 10syl313anc 1243 1  |-  ( ph  ->  mu )
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:  4atlem11  33592  dalem52  33707  dath2  33720  dalawlem1  33854  dalaw  33869  cdlemb2  34024  4atexlem7  34058  cdleme7ga  34231  cdleme18a  34274  cdleme18c  34276  cdleme21f  34315  cdleme26f2ALTN  34347  cdleme26f2  34348  cdleme27a  34350  cdlemg17dN  34646  cdlemg18a  34661  cdlemg31d  34683  cdlemg48  34720  cdlemj1  34804  dihord4  35242
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