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Theorem hadrot 1593
Description: Rotation law for the adder sum. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadrot (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

Proof of Theorem hadrot
StepHypRef Expression
1 hadcoma 1590 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2 hadcomb 1592 . 2 (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
31, 2bitri 276 1 (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 207  haddwhad 1584
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 208  df-xor 1496  df-had 1585
This theorem is referenced by:  had1  1595  sadadd2lem2  15787  saddisjlem  15801
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