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Mirrors > Home > MPE Home > Th. List > truxorfal | Structured version Visualization version GIF version |
Description: A ⊻ identity. (Contributed by David A. Wheeler, 8-May-2015.) |
Ref | Expression |
---|---|
truxorfal | ⊢ ((⊤ ⊻ ⊥) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1501 | . . 3 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ (⊤ ↔ ⊥)) | |
2 | trubifal 1564 | . . 3 ⊢ ((⊤ ↔ ⊥) ↔ ⊥) | |
3 | 1, 2 | xchbinx 336 | . 2 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ ⊥) |
4 | notfal 1561 | . 2 ⊢ (¬ ⊥ ↔ ⊤) | |
5 | 3, 4 | bitri 277 | 1 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ⊻ wxo 1500 ⊤wtru 1534 ⊥wfal 1545 |
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 209 df-xor 1501 df-tru 1536 df-fal 1546 |
This theorem is referenced by: falxortru 1580 |
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