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

Theorem nsyld 140
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 133 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ta ) )
41, 3syld 44 1  |-  ( ph  ->  ( ps  ->  -.  ta ) )
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:  pm2.65d  175  sbnOLD  2081  pltn2lp  15122  alexsubALTlem4  19464  ifeqeqx  25726  cvrat  32639
  Copyright terms: Public domain W3C validator