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Theorem syl123anc 1152
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 )
syl123anc.7  |-  ( ( ps  /\  ( ch 
/\  th )  /\  ( ta  /\  et  /\  ze ) )  ->  si )
Assertion
Ref Expression
syl123anc  |-  ( ph  ->  si )

Proof of Theorem syl123anc
StepHypRef Expression
1 sylXanc.1 . 2  |-  ( ph  ->  ps )
2 sylXanc.2 . . 3  |-  ( ph  ->  ch )
3 sylXanc.3 . . 3  |-  ( ph  ->  th )
42, 3jca 290 . 2  |-  ( ph  ->  ( ch  /\  th ) )
5 sylXanc.4 . 2  |-  ( ph  ->  ta )
6 sylXanc.5 . 2  |-  ( ph  ->  et )
7 sylXanc.6 . 2  |-  ( ph  ->  ze )
8 syl123anc.7 . 2  |-  ( ( ps  /\  ( ch 
/\  th )  /\  ( ta  /\  et  /\  ze ) )  ->  si )
91, 4, 5, 6, 7, 8syl113anc 1147 1  |-  ( ph  ->  si )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    /\ w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by: (None)
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