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Mirrors > Home > ILE Home > Th. List > dfop | Unicode version |
Description: Value of an ordered pair when the arguments are sets, with the conclusion corresponding to Kuratowski's original definition. (Contributed by NM, 25-Jun-1998.) |
Ref | Expression |
---|---|
dfop.1 | |
dfop.2 |
Ref | Expression |
---|---|
dfop |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfop.1 | . 2 | |
2 | dfop.2 | . 2 | |
3 | dfopg 3568 | . 2 | |
4 | 1, 2, 3 | mp2an 416 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wcel 1433 cvv 2601 csn 3398 cpr 3399 cop 3401 |
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-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 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-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 df-op 3407 |
This theorem is referenced by: opid 3588 elop 3986 opi1 3987 opi2 3988 opeqsn 4007 opeqpr 4008 uniop 4010 op1stb 4227 xpsspw 4468 relop 4504 funopg 4954 |
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