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Mirrors > Home > MPE Home > Th. List > trunorfalOLD | Structured version Visualization version GIF version |
Description: Obsolete version of trunorfal 1587 as of 17-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
trunorfalOLD | ⊢ ((⊤ ⊽ ⊥) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nor 1520 | . 2 ⊢ ((⊤ ⊽ ⊥) ↔ ¬ (⊤ ∨ ⊥)) | |
2 | tru 1540 | . . . . 5 ⊢ ⊤ | |
3 | 2 | orci 861 | . . . 4 ⊢ (⊤ ∨ ⊥) |
4 | 3 | notnoti 145 | . . 3 ⊢ ¬ ¬ (⊤ ∨ ⊥) |
5 | 4 | bifal 1552 | . 2 ⊢ (¬ (⊤ ∨ ⊥) ↔ ⊥) |
6 | 1, 5 | bitri 277 | 1 ⊢ ((⊤ ⊽ ⊥) ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ∨ wo 843 ⊽ wnor 1519 ⊤wtru 1537 ⊥wfal 1548 |
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 209 df-or 844 df-nor 1520 df-tru 1539 df-fal 1549 |
This theorem is referenced by: (None) |
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