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Mirrors > Home > ILE Home > Th. List > prid2 | Unicode version |
Description: An unordered pair contains its second member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
prid2.1 |
Ref | Expression |
---|---|
prid2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prid2.1 | . . 3 | |
2 | 1 | prid1 3498 | . 2 |
3 | prcom 3468 | . 2 | |
4 | 2, 3 | eleqtri 2153 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1433 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-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-v 2603 df-un 2977 df-sn 3404 df-pr 3405 |
This theorem is referenced by: prel12 3563 opi2 3988 opeluu 4200 ontr2exmid 4268 onsucelsucexmid 4273 regexmidlemm 4275 ordtri2or2exmid 4314 dmrnssfld 4613 funopg 4954 acexmidlema 5523 acexmidlemcase 5527 acexmidlem2 5529 2dom 6308 cnelprrecn 7109 mnfxr 8848 m1expcl2 9498 bdop 10666 |
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