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Theorem ecase23d 1285
 Description: Deduction for elimination by cases. (Contributed by NM, 22-Apr-1994.)
Hypotheses
Ref Expression
ecase23d.1 (φ → ¬ χ)
ecase23d.2 (φ → ¬ θ)
ecase23d.3 (φ → (ψ χ θ))
Assertion
Ref Expression
ecase23d (φψ)

Proof of Theorem ecase23d
StepHypRef Expression
1 ecase23d.1 . . 3 (φ → ¬ χ)
2 ecase23d.2 . . 3 (φ → ¬ θ)
3 ioran 476 . . 3 (¬ (χ θ) ↔ (¬ χ ¬ θ))
41, 2, 3sylanbrc 645 . 2 (φ → ¬ (χ θ))
5 ecase23d.3 . . . 4 (φ → (ψ χ θ))
6 3orass 937 . . . 4 ((ψ χ θ) ↔ (ψ (χ θ)))
75, 6sylib 188 . . 3 (φ → (ψ (χ θ)))
87ord 366 . 2 (φ → (¬ ψ → (χ θ)))
94, 8mt3d 117 1 (φψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∨ w3o 933 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  df-an 360  df-3or 935 This theorem is referenced by:  tfinltfin  4501
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