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Mirrors > Home > MPE Home > Th. List > xorneg | Structured version Visualization version GIF version |
Description: The connector ⊻ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
xorneg | ⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑 ⊻ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xorneg1 1518 | . 2 ⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓)) | |
2 | xorneg2 1517 | . . 3 ⊢ ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ 𝜓)) | |
3 | 2 | con2bii 358 | . 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓)) |
4 | 1, 3 | bitr4i 277 | 1 ⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑 ⊻ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ⊻ wxo 1506 |
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 206 df-xor 1507 |
This theorem is referenced by: (None) |
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