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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 8058. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-resscn |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cr 8009 |
. 2
| |
| 2 | cc 8008 |
. 2
| |
| 3 | 1, 2 | wss 3197 |
1
|
| Colors of variables: wff set class |
| This axiom is referenced by: recn 8143 reex 8144 recni 8169 rerecapb 9001 nnsscn 9126 nn0sscn 9385 qsscn 9838 reexpcl 10790 rpexpcl 10792 reexpclzap 10793 expge0 10809 expge1 10810 abscn2 11842 recn2 11844 imcn2 11845 climabs 11847 climre 11849 climim 11850 climcvg1nlem 11876 fsumrecl 11928 fsumrpcl 11931 fsumge0 11986 fsumre 11999 fsumim 12000 fprodrecl 12135 fprodrpcl 12138 fprodreclf 12141 fprodge0 12164 fprodge1 12166 reeff1 12227 remet 15238 tgioo2cntop 15247 tgioo2 15249 abscncf 15275 recncf 15276 imcncf 15277 cnrehmeocntop 15300 maxcncf 15305 mincncf 15306 ivthreinc 15335 hovercncf 15336 limcimolemlt 15354 recnprss 15377 dvidrelem 15382 dvidre 15387 dvcjbr 15398 dvfre 15400 reeff1olem 15461 cosz12 15470 ioocosf1o 15544 |
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