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Mirrors > Home > ILE Home > Th. List > dfpr2 | Unicode version |
Description: Alternate definition of unordered pair. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.) |
Ref | Expression |
---|---|
dfpr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3590 | . 2 | |
2 | elun 3268 | . . . 4 | |
3 | velsn 3600 | . . . . 5 | |
4 | velsn 3600 | . . . . 5 | |
5 | 3, 4 | orbi12i 759 | . . . 4 |
6 | 2, 5 | bitri 183 | . . 3 |
7 | 6 | abbi2i 2285 | . 2 |
8 | 1, 7 | eqtri 2191 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 703 wceq 1348 wcel 2141 cab 2156 cun 3119 csn 3583 cpr 3584 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 |
This theorem is referenced by: elprg 3603 nfpr 3633 pwsnss 3790 minmax 11193 xrminmax 11228 |
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