Description: Similar to dvelim with first hypothesis replaced by a distinct variable condition. Usage of this theorem is discouraged because it depends on ax-13 . Check out dvelimhw for a version requiring fewer axioms. (Contributed by NM, 25-Jul-2015) (Proof shortened by Wolf Lammen, 30-Apr-2018) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | dvelimv.1 | |- ( z = y -> ( ph <-> ps ) ) |
|
| Assertion | dvelimv | |- ( -. A. x x = y -> ( ps -> A. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dvelimv.1 | |- ( z = y -> ( ph <-> ps ) ) |
|
| 2 | ax-5 | |- ( ph -> A. x ph ) |
|
| 3 | 2 1 | dvelim | |- ( -. A. x x = y -> ( ps -> A. x ps ) ) |