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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 8227. (Contributed by NM, 1-Mar-1995.) |
| Ref | Expression |
|---|---|
| ax-resscn |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cr 8178 |
. 2
| |
| 2 | cc 8177 |
. 2
| |
| 3 | 1, 2 | wss 3220 |
1
|
| Colors of variables: wff set class |
| This axiom is used by: recn 8312 reex 8313 recni 8338 rerecapb 9173 nnsscn 9309 nn0sscn 9568 qsscn 10031 reexpcl 10993 rpexpcl 10995 reexpclzap 10996 expge0 11012 expge1 11013 abscn2 12081 recn2 12083 imcn2 12084 climabs 12086 climre 12088 climim 12089 climcvg1nlem 12115 fsumrecl 12168 fsumrpcl 12171 fsumge0 12226 fsumre 12239 fsumim 12240 fprodrecl 12375 fprodrpcl 12378 fprodreclf 12381 fprodge0 12404 fprodge1 12406 reeff1 12467 remet 15649 tgioo2cntop 15658 tgioo2 15660 abscncf 15686 recncf 15687 imcncf 15688 cnrehmeocntop 15711 maxcncf 15716 mincncf 15717 ivthreinc 15746 hovercncf 15747 limcimolemlt 15765 recnprss 15788 dvidrelem 15793 dvidre 15798 dvcjbr 15809 dvfre 15811 reeff1olem 15872 cosz12 15881 ioocosf1o 15955 |
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