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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 1508 | . . 3 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ (⊤ ↔ ⊥)) | |
2 | trubifal 1574 | . . 3 ⊢ ((⊤ ↔ ⊥) ↔ ⊥) | |
3 | 1, 2 | xchbinx 337 | . 2 ⊢ ((⊤ ⊻ ⊥) ↔ ¬ ⊥) |
4 | notfal 1571 | . 2 ⊢ (¬ ⊥ ↔ ⊤) | |
5 | 3, 4 | bitri 278 | 1 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ⊻ wxo 1507 ⊤wtru 1544 ⊥wfal 1555 |
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 df-tru 1546 df-fal 1556 |
This theorem is referenced by: falxortru 1590 |
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