| Intuitionistic Logic Explorer | 
      
      
      < Previous  
      Next >
      
       Nearby theorems  | 
  ||
| 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 7927. (Contributed by NM, 1-Mar-1995.) | 
| Ref | Expression | 
|---|---|
| ax-resscn | 
 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cr 7878 | 
. 2
 | |
| 2 | cc 7877 | 
. 2
 | |
| 3 | 1, 2 | wss 3157 | 
1
 | 
| Colors of variables: wff set class | 
| This axiom is referenced by: recn 8012 reex 8013 recni 8038 rerecapb 8870 nnsscn 8995 nn0sscn 9254 qsscn 9705 reexpcl 10648 rpexpcl 10650 reexpclzap 10651 expge0 10667 expge1 10668 abscn2 11480 recn2 11482 imcn2 11483 climabs 11485 climre 11487 climim 11488 climcvg1nlem 11514 fsumrecl 11566 fsumrpcl 11569 fsumge0 11624 fsumre 11637 fsumim 11638 fprodrecl 11773 fprodrpcl 11776 fprodreclf 11779 fprodge0 11802 fprodge1 11804 reeff1 11865 remet 14784 tgioo2cntop 14793 tgioo2 14795 abscncf 14821 recncf 14822 imcncf 14823 cnrehmeocntop 14846 maxcncf 14851 mincncf 14852 ivthreinc 14881 hovercncf 14882 limcimolemlt 14900 recnprss 14923 dvidrelem 14928 dvidre 14933 dvcjbr 14944 dvfre 14946 reeff1olem 15007 cosz12 15016 ioocosf1o 15090 | 
| Copyright terms: Public domain | W3C validator |