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Theorem mtord 641
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 → (χ θ)))
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 → (χ θ)))
4 df-or 359 . . . 4 ((χ θ) ↔ (¬ χθ))
53, 4syl6ib 217 . . 3 (φ → (ψ → (¬ χθ)))
62, 5mpid 37 . 2 (φ → (ψθ))
71, 6mtod 168 1 (φ → ¬ ψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wo 357
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 177  df-or 359
This theorem is referenced by: (None)
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