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Theorem 4cases 917
 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 767 . 2
4 4cases.2 . . 3
5 4cases.4 . . 3
64, 5pm2.61ian 767 . 2
73, 6pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360 This theorem is referenced by:  4casesdan  918  ax11eq  2272  ax11el  2273  suc11reg  7576  hasheqf1oi  11637  sizeusglecusg  21497  hashnbgravdg  21684  axlowdimlem15  25897  cdleme27a  31226 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 179  df-an 362
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