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Mirrors > Home > ILE Home > Th. List > opthpr | Unicode version |
Description: A way to represent ordered pairs using unordered pairs with distinct members. (Contributed by NM, 27-Mar-2007.) |
Ref | Expression |
---|---|
preq12b.1 | |
preq12b.2 | |
preq12b.3 | |
preq12b.4 |
Ref | Expression |
---|---|
opthpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq12b.1 | . . 3 | |
2 | preq12b.2 | . . 3 | |
3 | preq12b.3 | . . 3 | |
4 | preq12b.4 | . . 3 | |
5 | 1, 2, 3, 4 | preq12b 3562 | . 2 |
6 | idd 21 | . . . 4 | |
7 | df-ne 2246 | . . . . . 6 | |
8 | pm2.21 579 | . . . . . 6 | |
9 | 7, 8 | sylbi 119 | . . . . 5 |
10 | 9 | impd 251 | . . . 4 |
11 | 6, 10 | jaod 669 | . . 3 |
12 | orc 665 | . . 3 | |
13 | 11, 12 | impbid1 140 | . 2 |
14 | 5, 13 | syl5bb 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wo 661 wceq 1284 wcel 1433 wne 2245 cvv 2601 cpr 3399 |
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-in2 577 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-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 |
This theorem is referenced by: (None) |
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