MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nsyli Structured version   Unicode version

Theorem nsyli 146
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 138 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
41, 3syl5 33 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  2641  tz7.7  5468  tz7.48-2  7167  tz7.49  7170  php  7762  nndomo  7772  elirrv  8112  setind  8217  zorn2lem3  8926  alephval2  8995  inar1  9199  dfon2lem6  30221  sltres  30338  finminlem  30759  onint1  30894  poimirlem4  31647
  Copyright terms: Public domain W3C validator