Description: A commutation law for restricted universal quantifiers that swaps the domains of the restriction. (Contributed by NM, 22-Feb-2004) (Proof shortened by Wolf Lammen, 22-Dec-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ralcom3 | |- ( A. x e. A ( x e. B -> ph ) <-> A. x e. B ( x e. A -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bi2.04 | |- ( ( x e. A -> ( x e. B -> ph ) ) <-> ( x e. B -> ( x e. A -> ph ) ) ) |
|
| 2 | 1 | ralbii2 | |- ( A. x e. A ( x e. B -> ph ) <-> A. x e. B ( x e. A -> ph ) ) |