NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  hadbi123d Unicode version

Theorem hadbi123d 1382
Description: Equality theorem for half adder. (Contributed by Mario Carneiro, 4-Sep-2016.)
Hypotheses
Ref Expression
hadbid.1
hadbid.2
hadbid.3
Assertion
Ref Expression
hadbi123d hadd hadd

Proof of Theorem hadbi123d
StepHypRef Expression
1 hadbid.1 . . . 4
2 hadbid.2 . . . 4
31, 2xorbi12d 1315 . . 3  \/_  \/_
4 hadbid.3 . . 3
53, 4xorbi12d 1315 . 2 
\/_  \/_  \/_  \/_
6 df-had 1380 . 2 hadd  \/_  \/_
7 df-had 1380 . 2 hadd  \/_  \/_
85, 6, 73bitr4g 279 1 hadd hadd
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176    \/_ wxo 1304  haddwhad 1378
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 177  df-xor 1305  df-had 1380
This theorem is referenced by:  hadbi123i  1384
  Copyright terms: Public domain W3C validator