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Theorem nsyl4 142
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 129 . 2  |-  ( -. 
ch  ->  ph )
3 nsyl4.1 . 2  |-  ( ph  ->  ps )
42, 3syl 16 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  897  axc7  1847  ax10  2212  axc5c711  2234  axc5c711to11  2237  naecoms-o  2243  moanim  2336  moexex  2349  nfunsn  5887  card2on  7983  carden2a  8350  wwlknfi  24716  axc5c4c711  31262  axc5c4c711to11  31266  afvco2  32215  bj-naecomsv  34201
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