| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > altru | Structured version Visualization version GIF version | ||
| Description: For all sets, ⊤ is true. (Contributed by Anthony Hart, 13-Sep-2011.) |
| Ref | Expression |
|---|---|
| altru | ⊢ ∀𝑥⊤ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tru 1544 | . 2 ⊢ ⊤ | |
| 2 | 1 | ax-gen 1795 | 1 ⊢ ∀𝑥⊤ |
| Colors of variables: wff setvar class |
| Syntax hints: ∀wal 1538 ⊤wtru 1541 |
| 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 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |