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Mirrors > Home > ILE Home > Th. List > opabss | Unicode version |
Description: The collection of ordered pairs in a class is a subclass of it. (Contributed by NM, 27-Dec-1996.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-opab 3840 | . 2 | |
2 | df-br 3786 | . . . . 5 | |
3 | eleq1 2141 | . . . . . 6 | |
4 | 3 | biimpar 291 | . . . . 5 |
5 | 2, 4 | sylan2b 281 | . . . 4 |
6 | 5 | exlimivv 1817 | . . 3 |
7 | 6 | abssi 3069 | . 2 |
8 | 1, 7 | eqsstri 3029 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wex 1421 wcel 1433 cab 2067 wss 2973 cop 3401 class class class wbr 3785 copab 3838 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-in 2979 df-ss 2986 df-br 3786 df-opab 3840 |
This theorem is referenced by: (None) |
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