Description: Ordinal zero is less than every non-zero ordinal. Theorem 1.10 of Schloeder p. 2. Closely related to ord0eln0 . (Contributed by RP, 16-Jan-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ordne0gt0 | |- ( ( Ord A /\ A =/= (/) ) -> (/) e. A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ord0eln0 | |- ( Ord A -> ( (/) e. A <-> A =/= (/) ) ) |
|
| 2 | 1 | biimpar | |- ( ( Ord A /\ A =/= (/) ) -> (/) e. A ) |