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Theorem ecase3d 1030
 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 → (¬ (𝜓𝜒) → 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 856 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
4 ecase3d.3 . 2 (𝜑 → (¬ (𝜓𝜒) → 𝜃))
53, 4pm2.61d 182 1 (𝜑𝜃)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844 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 210  df-or 845 This theorem is referenced by:  ecased  1031  distrlem4pr  10446  lcmdvds  15950  atcvat4i  30186  cvrat4  36687  metakunt13  39311
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