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Theorem 3ecase 1470
Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)
Hypotheses
Ref Expression
3ecase.1 𝜑𝜃)
3ecase.2 𝜓𝜃)
3ecase.3 𝜒𝜃)
3ecase.4 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3ecase 𝜃

Proof of Theorem 3ecase
StepHypRef Expression
1 3ecase.4 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213exp 1115 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
3 3ecase.1 . . . 4 𝜑𝜃)
432a1d 26 . . 3 𝜑 → (𝜓 → (𝜒𝜃)))
52, 4pm2.61i 184 . 2 (𝜓 → (𝜒𝜃))
6 3ecase.2 . 2 𝜓𝜃)
7 3ecase.3 . 2 𝜒𝜃)
85, 6, 7pm2.61nii 186 1 𝜃
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by: (None)
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