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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 2046 | . . 3 | |
2 | eleq1 2100 | . . 3 | |
3 | negeq 7204 | . . . 4 | |
4 | 3 | eleq1d 2106 | . . 3 |
5 | 1, 2, 4 | 3orbi123d 1206 | . 2 |
6 | df-z 8246 | . 2 | |
7 | 5, 6 | elrab2 2700 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 w3o 884 wceq 1243 wcel 1393 cr 6888 cc0 6889 cneg 7183 cn 7914 cz 8245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-rab 2315 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-neg 7185 df-z 8246 |
This theorem is referenced by: nnnegz 8248 zre 8249 elnnz 8255 0z 8256 elnn0z 8258 elznn0nn 8259 elznn0 8260 elznn 8261 znegcl 8276 zaddcl 8285 ztri3or0 8287 zeo 8343 |
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