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Mirrors > Home > ILE Home > Th. List > nn0cnd | Unicode version |
Description: A nonnegative integer is a complex number. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nn0red.1 |
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Ref | Expression |
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nn0cnd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0red.1 |
. . 3
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2 | 1 | nn0red 8929 |
. 2
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3 | 2 | recnd 7712 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-cnex 7630 ax-resscn 7631 ax-1re 7633 ax-addrcl 7636 ax-rnegex 7648 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-sn 3497 df-int 3736 df-inn 8625 df-n0 8876 |
This theorem is referenced by: modsumfzodifsn 10056 addmodlteq 10058 uzennn 10096 expaddzaplem 10223 expaddzap 10224 expmulzap 10226 nn0le2msqd 10352 nn0opthlem1d 10353 nn0opthd 10355 nn0opth2d 10356 facdiv 10371 bcp1n 10394 bcn2m1 10402 bcn2p1 10403 omgadd 10435 fihashssdif 10451 hashdifpr 10453 hashxp 10459 zfz1isolemsplit 10468 zfz1isolem1 10470 fsumconst 11109 hash2iun1dif1 11135 binomlem 11138 bcxmas 11144 arisum 11153 arisum2 11154 mertensabs 11192 effsumlt 11243 dvdsexp 11401 nn0ob 11447 divalglemnn 11457 divalgmod 11466 bezoutlemnewy 11524 bezoutlema 11527 bezoutlemb 11528 mulgcd 11544 absmulgcd 11545 mulgcdr 11546 gcddiv 11547 lcmgcd 11599 lcmid 11601 lcm1 11602 3lcm2e6woprm 11607 6lcm4e12 11608 mulgcddvds 11615 qredeu 11618 divgcdcoprm0 11622 divgcdcoprmex 11623 cncongr1 11624 cncongr2 11625 pw2dvdseulemle 11684 phiprmpw 11737 |
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