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Theorem nsyli 141
Description: A negated syllogism inference. (Contributed by NM, 3-May-1994.)
Hypotheses
Ref Expression
nsyli.1  |-  ( ph  ->  ( ps  ->  ch ) )
nsyli.2  |-  ( th 
->  -.  ch )
Assertion
Ref Expression
nsyli  |-  ( ph  ->  ( th  ->  -.  ps ) )

Proof of Theorem nsyli
StepHypRef Expression
1 nsyli.2 . 2  |-  ( th 
->  -.  ch )
2 nsyli.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32con3d 133 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
41, 3syl5 32 1  |-  ( ph  ->  ( th  ->  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  necon3ad  2677  tz7.7  4904  tz7.48-2  7107  tz7.49  7110  php  7701  nndomo  7711  elirrv  8022  setind  8164  zorn2lem3  8877  alephval2  8946  inar1  9152  dfon2lem6  28813  sltres  29017  onint1  29507  finminlem  29729
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