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Theorem hadass 1533
Description: Associative law for the adder sum. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadass (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓𝜒)))

Proof of Theorem hadass
StepHypRef Expression
1 df-had 1530 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ⊻ 𝜒))
2 xorass 1465 . 2 (((𝜑𝜓) ⊻ 𝜒) ↔ (𝜑 ⊻ (𝜓𝜒)))
31, 2bitri 264 1 (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wxo 1461  haddwhad 1529
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 1462  df-had 1530
This theorem is referenced by:  hadcomb  1536
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