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Mirrors > Home > ILE Home > Th. List > bitru | GIF version |
Description: A theorem is equivalent to truth. (Contributed by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
bitru.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
bitru | ⊢ (𝜑 ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitru.1 | . 2 ⊢ 𝜑 | |
2 | tru 1357 | . 2 ⊢ ⊤ | |
3 | 1, 2 | 2th 174 | 1 ⊢ (𝜑 ↔ ⊤) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 105 ⊤wtru 1354 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-tru 1356 |
This theorem is referenced by: truorfal 1406 falortru 1407 truimtru 1409 falimtru 1411 falimfal 1412 notfal 1414 trubitru 1415 falbifal 1418 |
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