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Mirrors > Home > MPE Home > Th. List > falbitru | Structured version Visualization version GIF version |
Description: A ↔ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.) |
Ref | Expression |
---|---|
falbitru | ⊢ ((⊥ ↔ ⊤) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tbtru 1550 | . 2 ⊢ (⊥ ↔ (⊥ ↔ ⊤)) | |
2 | 1 | bicomi 223 | 1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ⊤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-tru 1545 |
This theorem is referenced by: trubifal 1573 |
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