Description: There is a bijection between the set of positive integers and the Cartesian product of the set of positive integers with itself. (Contributed by Glauco Siliprandi, 11-Oct-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nnf1oxpnn | |- E. f f : NN -1-1-onto-> ( NN X. NN ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | xpnnen | |- ( NN X. NN ) ~~ NN |
|
| 2 | 1 | ensymi | |- NN ~~ ( NN X. NN ) |
| 3 | bren | |- ( NN ~~ ( NN X. NN ) <-> E. f f : NN -1-1-onto-> ( NN X. NN ) ) |
|
| 4 | 2 3 | mpbi | |- E. f f : NN -1-1-onto-> ( NN X. NN ) |