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Mirrors > Home > ILE 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 6725. (Contributed by NM, 28-Mar-1998.) |
Ref | Expression |
---|---|
df-en |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cen 6716 | . 2 | |
2 | vx | . . . . . 6 | |
3 | 2 | cv 1347 | . . . . 5 |
4 | vy | . . . . . 6 | |
5 | 4 | cv 1347 | . . . . 5 |
6 | vf | . . . . . 6 | |
7 | 6 | cv 1347 | . . . . 5 |
8 | 3, 5, 7 | wf1o 5197 | . . . 4 |
9 | 8, 6 | wex 1485 | . . 3 |
10 | 9, 2, 4 | copab 4049 | . 2 |
11 | 1, 10 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: relen 6722 bren 6725 enssdom 6740 |
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