theorem prelrn (A: set) (a b: nat): $ a, b e. A -> b e. Ran A $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elrn | b e. Ran A <-> E. x x, b e. A |
|
| 2 | preq1 | x = a -> x, b = a, b |
|
| 3 | 2 | eleq1d | x = a -> (x, b e. A <-> a, b e. A) |
| 4 | 3 | iexe | a, b e. A -> E. x x, b e. A |
| 5 | 1, 4 | sylibr | a, b e. A -> b e. Ran A |