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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 1300 | . 2 ⊢ ⊤ | |
3 | 1, 2 | 2th 173 | 1 ⊢ (𝜑 ↔ ⊤) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ⊤wtru 1297 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-tru 1299 |
This theorem is referenced by: truorfal 1349 falortru 1350 truimtru 1352 falimtru 1354 falimfal 1355 notfal 1357 trubitru 1358 falbifal 1361 |
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