Description: Obsolete version of ralcom3 as of 22-Dec-2024. (Contributed by NM, 22-Feb-2004) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ralcom3OLD | |- ( A. x e. A ( x e. B -> ph ) <-> A. x e. B ( x e. A -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.04 | |- ( ( x e. A -> ( x e. B -> ph ) ) -> ( x e. B -> ( x e. A -> ph ) ) ) |
|
| 2 | 1 | ralimi2 | |- ( A. x e. A ( x e. B -> ph ) -> A. x e. B ( x e. A -> ph ) ) |
| 3 | pm2.04 | |- ( ( x e. B -> ( x e. A -> ph ) ) -> ( x e. A -> ( x e. B -> ph ) ) ) |
|
| 4 | 3 | ralimi2 | |- ( A. x e. B ( x e. A -> ph ) -> A. x e. A ( x e. B -> ph ) ) |
| 5 | 2 4 | impbii | |- ( A. x e. A ( x e. B -> ph ) <-> A. x e. B ( x e. A -> ph ) ) |