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Theorem cadrot 1609
Description: Rotation law for the adder carry. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
cadrot (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))

Proof of Theorem cadrot
StepHypRef Expression
1 cadcoma 1607 . 2 (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜑, 𝜒))
2 cadcomb 1608 . 2 (cadd(𝜓, 𝜑, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))
31, 2bitri 277 1 (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 208  caddwcad 1601
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 209  df-an 399  df-or 844  df-3or 1083  df-3an 1084  df-xor 1499  df-cad 1602
This theorem is referenced by: (None)
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