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Mirrors > Home > ILE Home > Th. List > recni | Unicode version |
Description: A real number is a complex number. (Contributed by NM, 1-Mar-1995.) |
Ref | Expression |
---|---|
recni.1 |
Ref | Expression |
---|---|
recni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-resscn 7839 | . 2 | |
2 | recni.1 | . 2 | |
3 | 1, 2 | sselii 3137 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cc 7745 cr 7746 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-resscn 7839 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3120 df-ss 3127 |
This theorem is referenced by: resubcli 8155 ltapii 8527 nncni 8861 2cn 8922 3cn 8926 4cn 8929 5cn 8931 6cn 8933 7cn 8935 8cn 8937 9cn 8939 halfcn 9065 8th4div3 9070 nn0cni 9120 numltc 9341 sqge0i 10535 lt2sqi 10536 le2sqi 10537 sq11i 10538 sqrtmsq2i 11071 0.999... 11456 ef01bndlem 11691 sin4lt0 11701 eirraplem 11711 eirr 11713 egt2lt3 11714 sqrt2irraplemnn 12105 picn 13306 sinhalfpilem 13310 cosneghalfpi 13317 sinhalfpip 13339 sinhalfpim 13340 coshalfpip 13341 coshalfpim 13342 sincosq1sgn 13345 sincosq2sgn 13346 sincosq3sgn 13347 sincosq4sgn 13348 cosq23lt0 13352 coseq00topi 13354 sincosq1eq 13358 sincos4thpi 13359 tan4thpi 13360 sincos6thpi 13361 2logb9irrALT 13490 taupi 13842 |
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