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Mirrors > Home > ILE Home > Th. List > elprg | Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15, generalized. (Contributed by NM, 13-Sep-1995.) |
Ref | Expression |
---|---|
elprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2087 | . . 3 | |
2 | eqeq1 2087 | . . 3 | |
3 | 1, 2 | orbi12d 739 | . 2 |
4 | dfpr2 3417 | . 2 | |
5 | 3, 4 | elab2g 2740 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wo 661 wceq 1284 wcel 1433 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: elpr 3419 elpr2 3420 elpri 3421 eltpg 3438 prid1g 3496 preqr1g 3558 m1expeven 9523 maxclpr 10108 minmax 10112 |
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