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Theorem cadcomb 1463
Description: Commutative law for adder carry. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
cadcomb

Proof of Theorem cadcomb
StepHypRef Expression
1 3orcoma 981 . . 3
2 biid 236 . . . 4
3 biid 236 . . . 4
4 ancom 450 . . . 4
52, 3, 43orbi123i 1186 . . 3
61, 5bitri 249 . 2
7 cador 1458 . 2
8 cador 1458 . 2
96, 7, 83bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  \/w3o 972  caddwcad 1446
This theorem is referenced by:  cadrot  1464
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-or 370  df-an 371  df-3or 974  df-xor 1364  df-cad 1448
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