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Theorem 4casesdan 941
 Description: Deduction eliminating two antecedents from the four possible cases that result from their true/false combinations. (Contributed by NM, 19-Mar-2013.)
Hypotheses
Ref Expression
4casesdan.1
4casesdan.2
4casesdan.3
4casesdan.4
Assertion
Ref Expression
4casesdan

Proof of Theorem 4casesdan
StepHypRef Expression
1 4casesdan.1 . . 3
21expcom 435 . 2
3 4casesdan.2 . . 3
43expcom 435 . 2
5 4casesdan.3 . . 3
65expcom 435 . 2
7 4casesdan.4 . . 3
87expcom 435 . 2
92, 4, 6, 84cases 940 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369 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 This theorem is referenced by:  unxpdomlem3  7633  mndifsplit  18584  cdleme41snaw  34483  dihord  35272  dihjat  35431
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