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Theorem ecase 982
Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)
Hypotheses
Ref Expression
ecase.1 𝜑𝜒)
ecase.2 𝜓𝜒)
ecase.3 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ecase 𝜒

Proof of Theorem ecase
StepHypRef Expression
1 ecase.3 . . 3 ((𝜑𝜓) → 𝜒)
21ex 450 . 2 (𝜑 → (𝜓𝜒))
3 ecase.1 . 2 𝜑𝜒)
4 ecase.2 . 2 𝜓𝜒)
52, 3, 4pm2.61nii 178 1 𝜒
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384
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-an 386
This theorem is referenced by:  hashprb  13141  txindislem  21376  1to3vfriswmgr  27042
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