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Mirrors > Home > MPE Home > Th. List > falnorfal | Structured version Visualization version GIF version |
Description: A ⊽ identity. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 17-Dec-2023.) |
Ref | Expression |
---|---|
falnorfal | ⊢ ((⊥ ⊽ ⊥) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nor 1525 | . . 3 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ (⊥ ∨ ⊥)) | |
2 | falorfal 1581 | . . 3 ⊢ ((⊥ ∨ ⊥) ↔ ⊥) | |
3 | 1, 2 | xchbinx 333 | . 2 ⊢ ((⊥ ⊽ ⊥) ↔ ¬ ⊥) |
4 | notfal 1569 | . 2 ⊢ (¬ ⊥ ↔ ⊤) | |
5 | 3, 4 | bitri 274 | 1 ⊢ ((⊥ ⊽ ⊥) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∨ wo 843 ⊽ wnor 1524 ⊤wtru 1542 ⊥wfal 1553 |
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-or 844 df-nor 1525 df-tru 1544 df-fal 1554 |
This theorem is referenced by: (None) |
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