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Theorem ecase3d 909
Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
ecase3d.1 (φ → (ψθ))
ecase3d.2 (φ → (χθ))
ecase3d.3 (φ → (¬ (ψ χ) → θ))
Assertion
Ref Expression
ecase3d (φθ)

Proof of Theorem ecase3d
StepHypRef Expression
1 ecase3d.1 . . 3 (φ → (ψθ))
2 ecase3d.2 . . 3 (φ → (χθ))
31, 2jaod 369 . 2 (φ → ((ψ χ) → θ))
4 ecase3d.3 . 2 (φ → (¬ (ψ χ) → θ))
53, 4pm2.61d 150 1 (φθ)
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:  ecased  910
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