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Theorem nsyl4 134
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 121 . 2  |-  ( -. 
ch  ->  ph )
3 nsyl4.1 . 2  |-  ( ph  ->  ps )
42, 3syl 15 1  |-  ( -. 
ch  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  pm5.55  867  hbimd  1721  ax6o  1723  naecoms  1888  ax6  2086  ax467  2108  ax467to7  2111  naecoms-o  2117  nfunsn  5558  card2on  7268  carden2a  7599  ax4567  27601  ax4567to7  27605  afvco2  28037  ax9lem4  29143  ax9lem9  29148
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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