Description: Cancellation law for restricted unique existential quantification. (Contributed by Peter Mazsa, 12-Feb-2018) (Proof shortened by Wolf Lammen, 12-Jan-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | reuanid | |- ( E! x e. A ( x e. A /\ ph ) <-> E! x e. A ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ibar | |- ( x e. A -> ( ph <-> ( x e. A /\ ph ) ) ) |
|
| 2 | 1 | bicomd | |- ( x e. A -> ( ( x e. A /\ ph ) <-> ph ) ) |
| 3 | 2 | reubiia | |- ( E! x e. A ( x e. A /\ ph ) <-> E! x e. A ph ) |