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Theorem cadnot 1461
Description: The adder carry distributes over negation. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
cadnot

Proof of Theorem cadnot
StepHypRef Expression
1 3ioran 991 . . 3
2 ianor 488 . . . 4
3 ianor 488 . . . 4
4 ianor 488 . . . 4
52, 3, 43anbi123i 1185 . . 3
61, 5bitri 249 . 2
7 cador 1458 . . 3
87notbii 296 . 2
9 cadan 1459 . 2
106, 8, 93bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  \/w3o 972  /\w3a 973  caddwcad 1446
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-3an 975  df-xor 1364  df-cad 1448
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