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| Mirrors > Home > NFE Home > Th. List > df-en | Unicode version | ||
Description: Define the equinumerosity
relation. Definition of [Enderton] p. 129.
We define 
to be a binary relation rather than a connective, so
its arguments must be sets to be meaningful. This is acceptable because
we do not consider equinumerosity for proper classes. We derive the
usual definition as bren 6030. (Contributed by NM,
28-Mar-1998.) |
| Ref | Expression |
|---|---|
| df-en |
              |
,,| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cen 6028 |
. 2
 | |
| 2 | vx |
. . . . . 6
 | |
| 3 | 2 | cv 1641 |
. . . . 5
|
| 4 | vy |
. . . . . 6
| |
| 5 | 4 | cv 1641 |
. . . . 5
|
| 6 | vf |
. . . . . 6
| |
| 7 | 6 | cv 1641 |
. . . . 5
|
| 8 | 3, 5, 7 | wf1o 4780 |
. . . 4
 |
| 9 | 8, 6 | wex 1541 |
. . 3
|
| 10 | 9, 2, 4 | copab 4622 |
. 2
|
| 11 | 1, 10 | wceq 1642 |
1
|
| Colors of variables: wff setvar class |
| This definition is referenced by: bren 6030 enex 6031 |
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