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Theorem hadass 1494
Description: Associative law for the adder sum. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadass  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ph  \/_  ( ps  \/_  ch ) ) )

Proof of Theorem hadass
StepHypRef Expression
1 df-had 1491 . 2  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ( ph  \/_ 
ps )  \/_  ch ) )
2 xorass 1405 . 2  |-  ( ( ( ph  \/_  ps )  \/_  ch )  <->  ( ph  \/_  ( ps  \/_  ch ) ) )
31, 2bitri 253 1  |-  (hadd (
ph ,  ps ,  ch )  <->  ( ph  \/_  ( ps  \/_  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 188    \/_ wxo 1401  haddwhad 1490
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 189  df-xor 1402  df-had 1491
This theorem is referenced by:  hadcomb  1497
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