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Mirrors > Home > ILE Home > Th. List > opid | Unicode version |
Description: The ordered pair in Kuratowski's representation. (Contributed by FL, 28-Dec-2011.) |
Ref | Expression |
---|---|
opid.1 |
Ref | Expression |
---|---|
opid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3536 | . . . 4 | |
2 | 1 | eqcomi 2141 | . . 3 |
3 | 2 | preq2i 3599 | . 2 |
4 | opid.1 | . . 3 | |
5 | 4, 4 | dfop 3699 | . 2 |
6 | dfsn2 3536 | . 2 | |
7 | 3, 5, 6 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 cvv 2681 csn 3522 cpr 3523 cop 3525 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 |
This theorem is referenced by: dmsnsnsng 5011 funopg 5152 |
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