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Mirrors > Home > ILE Home > Th. List > zcn | Unicode version |
Description: An integer is a complex number. (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
zcn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zre 8249 | . 2 | |
2 | 1 | recnd 7054 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 cc 6887 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 ax-resscn 6976 |
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-in 2924 df-ss 2931 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: zsscn 8253 zaddcllempos 8282 peano2zm 8283 zaddcllemneg 8284 zaddcl 8285 zsubcl 8286 zrevaddcl 8295 zlem1lt 8300 zltlem1 8301 zapne 8315 zdiv 8328 zdivadd 8329 zdivmul 8330 zextlt 8332 zneo 8339 zeo2 8344 peano5uzti 8346 zindd 8356 divfnzn 8556 qmulz 8558 zq 8561 qaddcl 8570 qnegcl 8571 qmulcl 8572 qreccl 8576 fzen 8907 uzsubsubfz 8911 fz01en 8917 fzmmmeqm 8921 fzsubel 8923 fztp 8940 fzsuc2 8941 fzrev2 8947 fzrev3 8949 elfzp1b 8959 fzrevral 8967 fzrevral2 8968 fzrevral3 8969 fzshftral 8970 fzoaddel2 9049 fzosubel2 9051 eluzgtdifelfzo 9053 fzocatel 9055 elfzom1elp1fzo 9058 fzval3 9060 zpnn0elfzo1 9064 fzosplitprm1 9090 fzoshftral 9094 flqzadd 9140 2tnp1ge0ge0 9143 ceilid 9157 intfracq 9162 zmod10 9182 frecfzen2 9204 iseqshft2 9232 isermono 9237 expsubap 9302 zesq 9367 shftuz 9418 nnabscl 9696 climshftlemg 9823 climshft 9825 sqrt2irr 9878 |
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