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Mirrors > Home > ILE Home > Th. List > df-er | Unicode version |
Description: Define the equivalence relation predicate. Our notation is not standard. A formal notation doesn't seem to exist in the literature; instead only informal English tends to be used. The present definition, although somewhat cryptic, nicely avoids dummy variables. In dfer2 6107 we derive a more typical definition. We show that an equivalence relation is reflexive, symmetric, and transitive in erref 6126, ersymb 6120, and ertr 6121. (Contributed by NM, 4-Jun-1995.) (Revised by Mario Carneiro, 2-Nov-2015.) |
Ref | Expression |
---|---|
df-er |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | cR | . . 3 | |
3 | 1, 2 | wer 6103 | . 2 |
4 | 2 | wrel 4350 | . . 3 |
5 | 2 | cdm 4345 | . . . 4 |
6 | 5, 1 | wceq 1243 | . . 3 |
7 | 2 | ccnv 4344 | . . . . 5 |
8 | 2, 2 | ccom 4349 | . . . . 5 |
9 | 7, 8 | cun 2915 | . . . 4 |
10 | 9, 2 | wss 2917 | . . 3 |
11 | 4, 6, 10 | w3a 885 | . 2 |
12 | 3, 11 | wb 98 | 1 |
Colors of variables: wff set class |
This definition is referenced by: dfer2 6107 ereq1 6113 ereq2 6114 errel 6115 erdm 6116 ersym 6118 ertr 6121 xpiderm 6177 |
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