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| Mirrors > Home > ILE Home > Th. List > ax-resscn | Unicode version | ||
| Description: The real numbers are a subset of the complex numbers. Axiom for real and complex numbers, justified by Theorem axresscn 8177. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-resscn |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cr 8128 |
. 2
| |
| 2 | cc 8127 |
. 2
| |
| 3 | 1, 2 | wss 3213 |
1
|
| Colors of variables: wff set class |
| This axiom is referenced by: recn 8262 reex 8263 recni 8288 rerecapb 9119 nnsscn 9244 nn0sscn 9503 qsscn 9966 reexpcl 10922 rpexpcl 10924 reexpclzap 10925 expge0 10941 expge1 10942 abscn2 12004 recn2 12006 imcn2 12007 climabs 12009 climre 12011 climim 12012 climcvg1nlem 12038 fsumrecl 12091 fsumrpcl 12094 fsumge0 12149 fsumre 12162 fsumim 12163 fprodrecl 12298 fprodrpcl 12301 fprodreclf 12304 fprodge0 12327 fprodge1 12329 reeff1 12390 remet 15430 tgioo2cntop 15439 tgioo2 15441 abscncf 15467 recncf 15468 imcncf 15469 cnrehmeocntop 15492 maxcncf 15497 mincncf 15498 ivthreinc 15527 hovercncf 15528 limcimolemlt 15546 recnprss 15569 dvidrelem 15574 dvidre 15579 dvcjbr 15590 dvfre 15592 reeff1olem 15653 cosz12 15662 ioocosf1o 15736 |
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