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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-3xornot1 | Structured version Visualization version GIF version |
Description: Flipping the first input flips the triple xor. wl-3xorrot 35159 can rotate any input to the front, so flipping any one of them does the same. (Contributed by Wolf Lammen, 1-May-2024.) |
Ref | Expression |
---|---|
wl-3xornot1 | ⊢ (¬ hadd(𝜑, 𝜓, 𝜒) ↔ hadd(¬ 𝜑, 𝜓, 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-3xorbi 35155 | . 2 ⊢ (hadd(¬ 𝜑, 𝜓, 𝜒) ↔ (¬ 𝜑 ↔ (𝜓 ↔ 𝜒))) | |
2 | nbbn 389 | . . 3 ⊢ ((¬ 𝜑 ↔ (𝜓 ↔ 𝜒)) ↔ ¬ (𝜑 ↔ (𝜓 ↔ 𝜒))) | |
3 | wl-3xorbi 35155 | . . 3 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒))) | |
4 | 2, 3 | xchbinxr 339 | . 2 ⊢ ((¬ 𝜑 ↔ (𝜓 ↔ 𝜒)) ↔ ¬ hadd(𝜑, 𝜓, 𝜒)) |
5 | 1, 4 | bitr2i 279 | 1 ⊢ (¬ hadd(𝜑, 𝜓, 𝜒) ↔ hadd(¬ 𝜑, 𝜓, 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 haddwhad 1595 |
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 401 df-or 846 df-ifp 1060 df-xor 1504 df-tru 1542 df-had 1596 |
This theorem is referenced by: (None) |
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