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Theorem nsyl4 147
Description: A negated syllogism inference. (Contributed by NM, 15-Feb-1996.)
Hypotheses
Ref Expression
nsyl4.1  |-  ( ph  ->  ps )
nsyl4.2  |-  ( -. 
ph  ->  ch )
Assertion
Ref Expression
nsyl4  |-  ( -. 
ch  ->  ps )

Proof of Theorem nsyl4
StepHypRef Expression
1 nsyl4.2 . . 3  |-  ( -. 
ph  ->  ch )
21con1i 132 . 2  |-  ( -. 
ch  ->  ph )
3 nsyl4.1 . 2  |-  ( ph  ->  ps )
42, 3syl 17 1  |-  ( -. 
ch  ->  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:  pm5.55  905  axc7  1912  moanim  2325  moexex  2337  nfunsn  5909  mptrcl  5968  card2on  8072  carden2a  8402  wwlknfi  25452  bj-naecomsv  31305  ax10  32386  axc5c711  32408  axc5c711to11  32411  naecoms-o  32417  axc5c4c711  36610  axc5c4c711to11  36614  afvco2  38390
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