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Theorem hadnot 1460
Description: The half adder distributes over negation. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadnot

Proof of Theorem hadnot
StepHypRef Expression
1 xorneg 1375 . . . 4
2 biid 236 . . . 4
31, 2xorbi12i 1376 . . 3
4 xorneg2 1374 . . 3
53, 4bitr2i 250 . 2
6 df-had 1447 . . 3
76notbii 296 . 2
8 df-had 1447 . 2
95, 7, 83bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  \/_wxo 1363  haddwhad 1445
This theorem is referenced by:  had0  1471
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-xor 1364  df-had 1447
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