| Mathbox for Wolf Lammen |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-3xorbi2 | Structured version Visualization version GIF version | ||
| Description: Alternative form of wl-3xorbi 37474. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024.) |
| Ref | Expression |
|---|---|
| wl-3xorbi2 | ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ↔ 𝜓) ↔ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-3xorbi 37474 | . 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒))) | |
| 2 | biass 384 | . 2 ⊢ (((𝜑 ↔ 𝜓) ↔ 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒))) | |
| 3 | 1, 2 | bitr4i 278 | 1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ↔ 𝜓) ↔ 𝜒)) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 haddwhad 1593 |
| 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 207 df-an 396 df-or 849 df-ifp 1064 df-xor 1512 df-tru 1543 df-had 1594 |
| This theorem is referenced by: wl-3xorbi123d 37476 wl-3xorrot 37478 wl-3xorcoma 37479 wl-3xornot 37482 |
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