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Theorem syl9r 73
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
syl9r.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl9r.2  |-  ( th 
->  ( ch  ->  ta ) )
Assertion
Ref Expression
syl9r  |-  ( th 
->  ( ph  ->  ( ps  ->  ta ) ) )

Proof of Theorem syl9r
StepHypRef Expression
1 syl9r.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 syl9r.2 . . 3  |-  ( th 
->  ( ch  ->  ta ) )
31, 2syl9 72 . 2  |-  ( ph  ->  ( th  ->  ( ps  ->  ta ) ) )
43com12 30 1  |-  ( th 
->  ( ph  ->  ( ps  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  sylan9r  405  pm2.85dc  873  looinvdc  883  pclem6  1335  nfimd  1547  19.23t  1638  fununi  5159  dfimafn  5436  funimass3  5502  nnsub  8716
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