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Mirrors > Home > MPE Home > Th. List > tbtru | Structured version Visualization version GIF version |
Description: A proposition is equivalent to itself being equivalent to ⊤. (Contributed by Anthony Hart, 14-Aug-2011.) |
Ref | Expression |
---|---|
tbtru | ⊢ (𝜑 ↔ (𝜑 ↔ ⊤)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1541 | . 2 ⊢ ⊤ | |
2 | 1 | tbt 369 | 1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 ⊤wtru 1538 |
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 207 df-tru 1540 |
This theorem is referenced by: falbitru 1567 ab0orv 4389 tgcgr4 28554 iinabrex 32589 sgn3da 34523 wl-1xor 37465 wl-1mintru1 37471 prjspvs 42597 aistia 46847 |
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