Description: Obsolete version of raleleq as of 18-Jul-2025. (Contributed by AV, 30-Oct-2020) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | raleleqOLD | |- ( A = B -> A. x e. A x e. B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralel | |- A. x e. B x e. B |
|
| 2 | id | |- ( A = B -> A = B ) |
|
| 3 | 2 | raleqdv | |- ( A = B -> ( A. x e. A x e. B <-> A. x e. B x e. B ) ) |
| 4 | 1 3 | mpbiri | |- ( A = B -> A. x e. A x e. B ) |