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Mirrors > Home > MPE Home > Th. List > xor3 | Structured version Visualization version GIF version |
Description: Two ways to express "exclusive or". (Contributed by NM, 1-Jan-2006.) |
Ref | Expression |
---|---|
xor3 | ⊢ (¬ (𝜑 ↔ 𝜓) ↔ (𝜑 ↔ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.18 382 | . . 3 ⊢ ((𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓)) | |
2 | 1 | con2bii 357 | . 2 ⊢ ((𝜑 ↔ ¬ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓)) |
3 | 2 | bicomi 223 | 1 ⊢ (¬ (𝜑 ↔ 𝜓) ↔ (𝜑 ↔ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 |
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 |
This theorem is referenced by: nbbn 384 pm5.15 1010 nbi2 1013 xorass 1513 hadnot 1602 nabbi 3044 nmogtmnf 29420 nmopgtmnf 30518 limsucncmpi 34730 wl-3xorbi 35757 wl-3xornot 35765 aiffnbandciffatnotciffb 44758 axorbciffatcxorb 44759 abnotbtaxb 44769 afv2orxorb 45079 line2ylem 46456 line2xlem 46458 |
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