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Theorem hadbi 1454
Description: The half adder is the same as the triple biconditional. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadbi

Proof of Theorem hadbi
StepHypRef Expression
1 df-xor 1364 . 2
2 df-had 1447 . 2
3 xnor 1365 . . . 4
43bibi1i 314 . . 3
5 nbbn 358 . . 3
64, 5bitri 249 . 2
71, 2, 63bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  \/_wxo 1363  haddwhad 1445
This theorem is referenced by:  had1  1470
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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