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| Mirrors > Home > MPE Home > Th. List > sbtru | Structured version Visualization version GIF version | ||
| Description: The result of substituting in the truth constant "true" is true. (Contributed by BJ, 2-Sep-2023.) |
| Ref | Expression |
|---|---|
| sbtru | ⊢ [𝑦 / 𝑥]⊤ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tru 1544 | . 2 ⊢ ⊤ | |
| 2 | 1 | sbt 2067 | 1 ⊢ [𝑦 / 𝑥]⊤ |
| Colors of variables: wff setvar class |
| Syntax hints: ⊤wtru 1541 [wsb 2065 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 |
| This theorem depends on definitions: df-bi 207 df-tru 1543 df-sb 2066 |
| This theorem is referenced by: (None) |
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