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Mirrors > Home > ILE Home > Th. List > elz | Unicode version |
Description: Membership in the set of integers. (Contributed by NM, 8-Jan-2002.) |
Ref | Expression |
---|---|
elz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2124 | . . 3 | |
2 | eleq1 2180 | . . 3 | |
3 | negeq 7923 | . . . 4 | |
4 | 3 | eleq1d 2186 | . . 3 |
5 | 1, 2, 4 | 3orbi123d 1274 | . 2 |
6 | df-z 9023 | . 2 | |
7 | 5, 6 | elrab2 2816 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3o 946 wceq 1316 wcel 1465 cr 7587 cc0 7588 cneg 7902 cn 8688 cz 9022 |
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-3or 948 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-neg 7904 df-z 9023 |
This theorem is referenced by: nnnegz 9025 zre 9026 elnnz 9032 0z 9033 elnn0z 9035 elznn0nn 9036 elznn0 9037 elznn 9038 znegcl 9053 zaddcl 9062 ztri3or0 9064 zeo 9124 addmodlteq 10139 |
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