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Theorem syl9r 71
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 70 . 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-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  sylan9r  396  pm2.85dc  822  looinvdc  832  pclem6  1281  nfimd  1493  19.23t  1583  fununi  4995  dfimafn  5250  funimass3  5311  nnsub  8028
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