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Theorem ecase3d 1003
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 394 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
4 ecase3d.3 . 2 (𝜑 → (¬ (𝜓𝜒) → 𝜃))
53, 4pm2.61d 170 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382
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 197  df-or 384
This theorem is referenced by:  ecased  1004  distrlem4pr  9886  lcmdvds  15368  atcvat4i  29384  cvrat4  35047
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