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

Theorem nsyl3 556
Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.) (Revised by NM, 13-Jun-2013.)
Hypotheses
Ref Expression
nsyl3.1 (𝜑 → ¬ 𝜓)
nsyl3.2 (𝜒𝜓)
Assertion
Ref Expression
nsyl3 (𝜒 → ¬ 𝜑)

Proof of Theorem nsyl3
StepHypRef Expression
1 nsyl3.2 . 2 (𝜒𝜓)
2 nsyl3.1 . . 3 (𝜑 → ¬ 𝜓)
32a1i 9 . 2 (𝜒 → (𝜑 → ¬ 𝜓))
41, 3mt2d 555 1 (𝜒 → ¬ 𝜑)
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 544  ax-in2 545
This theorem is referenced by:  con2i  557  nsyl  558  pm2.65i  568  cesare  2004  cesaro  2008  pwnss  3909  sucprcreg  4267  reldmtpos  5855  fzn  8873
  Copyright terms: Public domain W3C validator