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Mirrors > Home > ILE Home > Th. List > tbtru | 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 1336 | . 2 ⊢ ⊤ | |
2 | 1 | tbt 246 | 1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ⊤wtru 1333 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-tru 1335 |
This theorem is referenced by: (None) |
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