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| 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 1544 | . 2 ⊢ ⊤ | |
| 2 | 1 | tbt 369 | 1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ↔ wb 206 ⊤wtru 1541 | 
| 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 1543 | 
| This theorem is referenced by: falbitru 1570 ab0orv 4383 tgcgr4 28539 iinabrex 32582 sgn3da 34544 wl-1xor 37483 wl-1mintru1 37489 prjspvs 42620 aistia 46909 | 
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