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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 2124 | . . 3 | |
2 | eqeq1 2124 | . . 3 | |
3 | 1, 2 | orbi12d 767 | . 2 |
4 | dfpr2 3516 | . 2 | |
5 | 3, 4 | elab2g 2804 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 682 wceq 1316 wcel 1465 cpr 3498 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 |
This theorem is referenced by: elpr 3518 elpr2 3519 elpri 3520 eltpg 3539 prid1g 3597 preqr1g 3663 m1expeven 10308 maxclpr 10962 minmax 10969 minclpr 10976 xrminmax 11002 |
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