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Theorem had1 1470
Description: If the first parameter is true, the half adder is equivalent to the equality of the other two inputs. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
had1

Proof of Theorem had1
StepHypRef Expression
1 hadbi 1454 . . 3
2 biass 359 . . 3
31, 2bitri 249 . 2
4 id 22 . . . 4
5 biidd 237 . . . 4
64, 52thd 240 . . 3
7 biass 359 . . 3
86, 7sylibr 212 . 2
93, 8syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  haddwhad 1445
This theorem is referenced by:  had0  1471  sadadd2lem2  14100
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
  Copyright terms: Public domain W3C validator