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

Theorem nsyld 577
Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
nsyld.1 (𝜑 → (𝜓 → ¬ 𝜒))
nsyld.2 (𝜑 → (𝜏𝜒))
Assertion
Ref Expression
nsyld (𝜑 → (𝜓 → ¬ 𝜏))

Proof of Theorem nsyld
StepHypRef Expression
1 nsyld.1 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
2 nsyld.2 . . 3 (𝜑 → (𝜏𝜒))
32con3d 561 . 2 (𝜑 → (¬ 𝜒 → ¬ 𝜏))
41, 3syld 40 1 (𝜑 → (𝜓 → ¬ 𝜏))
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:  pm2.65d  586  fzdcel  8871
  Copyright terms: Public domain W3C validator