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Theorem mtord 693
Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.)
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.2 . 2 (𝜑 → ¬ 𝜃)
2 mtord.1 . . 3 (𝜑 → ¬ 𝜒)
3 mtord.3 . . . 4 (𝜑 → (𝜓 → (𝜒𝜃)))
4 df-or 384 . . . 4 ((𝜒𝜃) ↔ (¬ 𝜒𝜃))
53, 4syl6ib 241 . . 3 (𝜑 → (𝜓 → (¬ 𝜒𝜃)))
62, 5mpid 44 . 2 (𝜑 → (𝜓𝜃))
71, 6mtod 189 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 384
This theorem is referenced by:  swoer  7817  inar1  9635
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