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Mirrors > Home > MPE Home > Th. List > falxortru | Structured version Visualization version GIF version |
Description: A ⊻ identity. (Contributed by David A. Wheeler, 9-May-2015.) (Proof shortened by Wolf Lammen, 10-Jul-2020.) |
Ref | Expression |
---|---|
falxortru | ⊢ ((⊥ ⊻ ⊤) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xorcom 1509 | . 2 ⊢ ((⊥ ⊻ ⊤) ↔ (⊤ ⊻ ⊥)) | |
2 | truxorfal 1588 | . 2 ⊢ ((⊤ ⊻ ⊥) ↔ ⊤) | |
3 | 1, 2 | bitri 274 | 1 ⊢ ((⊥ ⊻ ⊤) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ↔ 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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