MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  hadrot Structured version   Visualization version   GIF version

Theorem hadrot 1539
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 1537 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2 hadcomb 1538 . 2 (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
31, 2bitri 264 1 (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 196  haddwhad 1531
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 197  df-xor 1464  df-had 1532
This theorem is referenced by:  had1  1541  sadadd2lem2  15166  saddisjlem  15180
  Copyright terms: Public domain W3C validator