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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 3585 | . . . 4 | |
2 | 1 | eqcomi 2168 | . . 3 |
3 | 2 | preq2i 3652 | . 2 |
4 | opid.1 | . . 3 | |
5 | 4, 4 | dfop 3752 | . 2 |
6 | dfsn2 3585 | . 2 | |
7 | 3, 5, 6 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cvv 2722 csn 3571 cpr 3572 cop 3574 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-un 3116 df-sn 3577 df-pr 3578 df-op 3580 |
This theorem is referenced by: dmsnsnsng 5076 funopg 5217 |
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