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Mirrors > Home > MPE Home > Th. List > xnor | Structured version Visualization version GIF version |
Description: Two ways to write XNOR (exclusive not-or). (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
xnor | ⊢ ((𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ⊻ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1508 | . 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓)) | |
2 | 1 | con2bii 361 | 1 ⊢ ((𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ⊻ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ⊻ wxo 1507 |
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-xor 1508 |
This theorem is referenced by: xorass 1512 xorneg2 1518 hadbi 1604 had0 1611 wl-df-3xor 35376 wl-3xorbi 35381 tsxo1 36032 tsxo2 36033 |
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