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Theorem 4cases 949
Description: Inference eliminating two antecedents from the four possible cases that result from their true/false combinations. (Contributed by NM, 25-Oct-2003.)
Hypotheses
Ref Expression
4cases.1
4cases.2
4cases.3
4cases.4
Assertion
Ref Expression
4cases

Proof of Theorem 4cases
StepHypRef Expression
1 4cases.1 . . 3
2 4cases.3 . . 3
31, 2pm2.61ian 790 . 2
4 4cases.2 . . 3
5 4cases.4 . . 3
64, 5pm2.61ian 790 . 2
73, 6pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369
This theorem is referenced by:  4casesdan  950  ax12eq  2271  ax12el  2272  suc11reg  8057  hasheqf1oi  12424  axlowdimlem15  24259  sizeusglecusg  24486  hashnbgravdg  24913  cdleme27a  36093
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
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