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Theorem 3ecase 1333
Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)
Hypotheses
Ref Expression
3ecase.1
3ecase.2
3ecase.3
3ecase.4
Assertion
Ref Expression
3ecase

Proof of Theorem 3ecase
StepHypRef Expression
1 3ecase.4 . . . 4
213exp 1195 . . 3
3 3ecase.1 . . . . 5
43a1d 25 . . . 4
54a1d 25 . . 3
62, 5pm2.61i 164 . 2
7 3ecase.2 . 2
8 3ecase.3 . 2
96, 7, 8pm2.61nii 166 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\w3a 973
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 185  df-an 371  df-3an 975
  Copyright terms: Public domain W3C validator