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Theorem nsyld 132
Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
nsyld.1  |-  ( ph  ->  ( ps  ->  -.  ch ) )
nsyld.2  |-  ( ph  ->  ( ta  ->  ch ) )
Assertion
Ref Expression
nsyld  |-  ( ph  ->  ( ps  ->  -.  ta ) )

Proof of Theorem nsyld
StepHypRef Expression
1 nsyld.1 . 2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
2 nsyld.2 . . 3  |-  ( ph  ->  ( ta  ->  ch ) )
32con3d 125 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ta ) )
41, 3syld 40 1  |-  ( ph  ->  ( ps  ->  -.  ta ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  pm2.65d  166  sbn  2015  pltn2lp  14119  alexsubALTlem4  17760  sbnNEW7  29537  cvrat  30233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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