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Theorem mtord 730
 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 582 . . . 4 (𝜑 → (𝜒 → ¬ 𝜓))
4 mtord.2 . . . . 5 (𝜑 → ¬ 𝜃)
54pm2.21d 582 . . . 4 (𝜑 → (𝜃 → ¬ 𝜓))
63, 5jaod 670 . . 3 (𝜑 → ((𝜒𝜃) → ¬ 𝜓))
71, 6syld 44 . 2 (𝜑 → (𝜓 → ¬ 𝜓))
87pm2.01d 581 1 (𝜑 → ¬ 𝜓)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 662 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  swoer  6250
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