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

Theorem mtord 778
Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypotheses
Ref Expression
mtord.1 (𝜑 → ¬ 𝜒)
mtord.2 (𝜑 → ¬ 𝜃)
mtord.3 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
mtord (𝜑 → ¬ 𝜓)

Proof of Theorem mtord
StepHypRef Expression
1 mtord.3 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
2 mtord.1 . . . . 5 (𝜑 → ¬ 𝜒)
32pm2.21d 614 . . . 4 (𝜑 → (𝜒 → ¬ 𝜓))
4 mtord.2 . . . . 5 (𝜑 → ¬ 𝜃)
54pm2.21d 614 . . . 4 (𝜑 → (𝜃 → ¬ 𝜓))
63, 5jaod 712 . . 3 (𝜑 → ((𝜒𝜃) → ¬ 𝜓))
71, 6syld 45 . 2 (𝜑 → (𝜓 → ¬ 𝜓))
87pm2.01d 613 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  swoer  6538
  Copyright terms: Public domain W3C validator