Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005) Avoid df-clel , ax-8 . (Revised by Gino Giotto, 2-Sep-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ral0 | |- A. x e. (/) ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid | |- (/) = (/) |
|
| 2 | rzal | |- ( (/) = (/) -> A. x e. (/) ph ) |
|
| 3 | 1 2 | ax-mp | |- A. x e. (/) ph |