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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 7920. (Contributed by NM, 1-Mar-1995.) |
Ref | Expression |
---|---|
ax-resscn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cr 7871 |
. 2
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2 | cc 7870 |
. 2
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3 | 1, 2 | wss 3153 |
1
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Colors of variables: wff set class |
This axiom is referenced by: recn 8005 reex 8006 recni 8031 rerecapb 8862 nnsscn 8987 nn0sscn 9245 qsscn 9696 reexpcl 10627 rpexpcl 10629 reexpclzap 10630 expge0 10646 expge1 10647 abscn2 11458 recn2 11460 imcn2 11461 climabs 11463 climre 11465 climim 11466 climcvg1nlem 11492 fsumrecl 11544 fsumrpcl 11547 fsumge0 11602 fsumre 11615 fsumim 11616 fprodrecl 11751 fprodrpcl 11754 fprodreclf 11757 fprodge0 11780 fprodge1 11782 reeff1 11843 remet 14708 tgioo2cntop 14717 abscncf 14740 recncf 14741 imcncf 14742 cnrehmeocntop 14764 maxcncf 14769 mincncf 14770 ivthreinc 14799 hovercncf 14800 limcimolemlt 14818 recnprss 14841 dvcjbr 14857 dvfre 14859 reeff1olem 14906 cosz12 14915 ioocosf1o 14989 |
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