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Theorem hadcoma 1388
Description: Commutative law for triple XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
hadcoma (hadd(φ, ψ, χ) ↔ hadd(ψ, φ, χ))

Proof of Theorem hadcoma
StepHypRef Expression
1 xorcom 1307 . . 3 ((φψ) ↔ (ψφ))
2 biid 227 . . 3 (χχ)
31, 2xorbi12i 1314 . 2 (((φψ) ⊻ χ) ↔ ((ψφ) ⊻ χ))
4 df-had 1380 . 2 (hadd(φ, ψ, χ) ↔ ((φψ) ⊻ χ))
5 df-had 1380 . 2 (hadd(ψ, φ, χ) ↔ ((ψφ) ⊻ χ))
63, 4, 53bitr4i 268 1 (hadd(φ, ψ, χ) ↔ hadd(ψ, φ, χ))
Colors of variables: wff setvar class
Syntax hints:  wb 176  wxo 1304  haddwhad 1378
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 177  df-xor 1305  df-had 1380
This theorem is referenced by:  hadrot  1390
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