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Theorem wl-3xornot1 34856
Description: Flipping the first input flips the triple xor. wl-3xorrot 34853 can rotate any input to the front, so flipping any one of them does the same. (Contributed by Wolf Lammen, 1-May-2024.)
Assertion
Ref Expression
wl-3xornot1 (¬ hadd(𝜑, 𝜓, 𝜒) ↔ hadd(¬ 𝜑, 𝜓, 𝜒))

Proof of Theorem wl-3xornot1
StepHypRef Expression
1 wl-3xorbi 34849 . 2 (hadd(¬ 𝜑, 𝜓, 𝜒) ↔ (¬ 𝜑 ↔ (𝜓𝜒)))
2 nbbn 388 . . 3 ((¬ 𝜑 ↔ (𝜓𝜒)) ↔ ¬ (𝜑 ↔ (𝜓𝜒)))
3 wl-3xorbi 34849 . . 3 (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓𝜒)))
42, 3xchbinxr 338 . 2 ((¬ 𝜑 ↔ (𝜓𝜒)) ↔ ¬ hadd(𝜑, 𝜓, 𝜒))
51, 4bitr2i 279 1 (¬ hadd(𝜑, 𝜓, 𝜒) ↔ hadd(¬ 𝜑, 𝜓, 𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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: (None)
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