Description: Closed theorem form of isset that does not require x and A to be distinct. Extracted from the proof of vtoclgft . (Contributed by Wolf Lammen, 9-Apr-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | issetft | |- ( F/_ x A -> ( A e. _V <-> E. x x = A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | isset | |- ( A e. _V <-> E. y y = A ) |
|
| 2 | cbvexeqsetf | |- ( F/_ x A -> ( E. x x = A <-> E. y y = A ) ) |
|
| 3 | 1 2 | bitr4id | |- ( F/_ x A -> ( A e. _V <-> E. x x = A ) ) |