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Theorem nsyl3 591
Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.)
Hypotheses
Ref Expression
nsyl3.1  |-  ( ph  ->  -.  ps )
nsyl3.2  |-  ( ch 
->  ps )
Assertion
Ref Expression
nsyl3  |-  ( ch 
->  -.  ph )

Proof of Theorem nsyl3
StepHypRef Expression
1 nsyl3.2 . 2  |-  ( ch 
->  ps )
2 nsyl3.1 . . 3  |-  ( ph  ->  -.  ps )
32a1i 9 . 2  |-  ( ch 
->  ( ph  ->  -.  ps ) )
41, 3mt2d 590 1  |-  ( ch 
->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 579  ax-in2 580
This theorem is referenced by:  con2i  592  nsyl  593  pm2.65i  603  cesare  2052  cesaro  2056  pwnss  3986  sucprcreg  4355  reg3exmidlemwe  4384  reldmtpos  6000  snexxph  6638  fzn  9425  seq3f1olemqsum  9894
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