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Mirrors > Home > MPE Home > Th. List > snnzg | Structured version Visualization version Unicode version |
Description: The singleton of a set is not empty. (Contributed by NM, 14-Dec-2008.) |
Ref | Expression |
---|---|
snnzg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 4206 | . 2 | |
2 | ne0i 3921 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wne 2794 c0 3915 csn 4177 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-v 3202 df-dif 3577 df-nul 3916 df-sn 4178 |
This theorem is referenced by: snnz 4309 0nelop 4960 frirr 5091 frsn 5189 1stconst 7265 2ndconst 7266 fczsupp0 7324 hashge3el3dif 13268 pwsbas 16147 pwsle 16152 trnei 21696 uffix 21725 neiflim 21778 hausflim 21785 flimcf 21786 flimclslem 21788 cnpflf2 21804 cnpflf 21805 fclsfnflim 21831 ustneism 22027 ustuqtop5 22049 neipcfilu 22100 dv11cn 23764 noextendseq 31820 scutbdaylt 31922 elpaddat 35090 elpadd2at 35092 snn0d 39258 ovnovollem3 40872 |
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