ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nsyl3 Unicode version

Theorem nsyl3 566
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 565 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 554  ax-in2 555
This theorem is referenced by:  con2i  567  nsyl  568  pm2.65i  578  cesare  2020  cesaro  2024  pwnss  3940  sucprcreg  4301  reg3exmidlemwe  4331  reldmtpos  5899  fzn  9008
  Copyright terms: Public domain W3C validator