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Mirrors > Home > MPE Home > Th. List > truxortru | Structured version Visualization version GIF version |
Description: A ⊻ identity. (Contributed by David A. Wheeler, 8-May-2015.) |
Ref | Expression |
---|---|
truxortru | ⊢ ((⊤ ⊻ ⊤) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1507 | . . 3 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤)) | |
2 | trubitru 1571 | . . 3 ⊢ ((⊤ ↔ ⊤) ↔ ⊤) | |
3 | 1, 2 | xchbinx 334 | . 2 ⊢ ((⊤ ⊻ ⊤) ↔ ¬ ⊤) |
4 | nottru 1569 | . 2 ⊢ (¬ ⊤ ↔ ⊥) | |
5 | 3, 4 | bitri 274 | 1 ⊢ ((⊤ ⊻ ⊤) ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ⊻ wxo 1506 ⊤wtru 1543 ⊥wfal 1554 |
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 df-tru 1545 df-fal 1555 |
This theorem is referenced by: (None) |
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