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Mirrors > Home > MPE Home > Th. List > trunorfal | 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 |
---|---|
trunorfal | ⊢ ((⊤ ⊽ ⊥) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nor 1527 | . . 3 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ (⊤ ∨ ⊥)) | |
2 | truorfal 1581 | . . 3 ⊢ ((⊤ ∨ ⊥) ↔ ⊤) | |
3 | 1, 2 | xchbinx 337 | . 2 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ ⊤) |
4 | df-fal 1556 | . 2 ⊢ (⊥ ↔ ¬ ⊤) | |
5 | 3, 4 | bitr4i 281 | 1 ⊢ ((⊤ ⊽ ⊥) ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ∨ wo 847 ⊽ wnor 1526 ⊤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-or 848 df-nor 1527 df-tru 1546 df-fal 1556 |
This theorem is referenced by: falnortru 1596 |
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