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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-df3xor3 | Structured version Visualization version GIF version |
Description: Alternative form of wl-df3xor2 35151. Copy of df-had 1596. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 1-May-2024.) |
Ref | Expression |
---|---|
wl-df3xor3 | ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ⊻ 𝜓) ⊻ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-df3xor2 35151 | . 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓 ⊻ 𝜒))) | |
2 | xorass 1508 | . 2 ⊢ (((𝜑 ⊻ 𝜓) ⊻ 𝜒) ↔ (𝜑 ⊻ (𝜓 ⊻ 𝜒))) | |
3 | 1, 2 | bitr4i 281 | 1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ⊻ 𝜓) ⊻ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ⊻ wxo 1503 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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