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Theorem wl-3xorrot 34887
Description: Rotation law for triple xor. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024.)
Assertion
Ref Expression
wl-3xorrot (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

Proof of Theorem wl-3xorrot
StepHypRef Expression
1 bicom 225 . 2 ((𝜑 ↔ (𝜓𝜒)) ↔ ((𝜓𝜒) ↔ 𝜑))
2 wl-3xorbi 34883 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓𝜒)))
3 wl-3xorbi2 34884 . 2 (hadd(𝜓, 𝜒, 𝜑) ↔ ((𝜓𝜒) ↔ 𝜑))
41, 2, 33bitr4i 306 1 (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 209  haddwhad 1594
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 210  df-an 400  df-or 845  df-ifp 1059  df-xor 1503  df-tru 1541  df-had 1595
This theorem is referenced by:  wl-3xorcomb  34889
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