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Theorem ecase2d 906
 Description: Deduction for elimination by cases. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Dec-2012.)
Hypotheses
Ref Expression
ecase2d.1 (φψ)
ecase2d.2 (φ → ¬ (ψ χ))
ecase2d.3 (φ → ¬ (ψ θ))
ecase2d.4 (φ → (τ (χ θ)))
Assertion
Ref Expression
ecase2d (φτ)

Proof of Theorem ecase2d
StepHypRef Expression
1 idd 21 . 2 (φ → (ττ))
2 ecase2d.1 . . . 4 (φψ)
3 ecase2d.2 . . . . 5 (φ → ¬ (ψ χ))
43pm2.21d 98 . . . 4 (φ → ((ψ χ) → τ))
52, 4mpand 656 . . 3 (φ → (χτ))
6 ecase2d.3 . . . . 5 (φ → ¬ (ψ θ))
76pm2.21d 98 . . . 4 (φ → ((ψ θ) → τ))
82, 7mpand 656 . . 3 (φ → (θτ))
95, 8jaod 369 . 2 (φ → ((χ θ) → τ))
10 ecase2d.4 . 2 (φ → (τ (χ θ)))
111, 9, 10mpjaod 370 1 (φτ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360 This theorem is referenced by: (None)
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