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| Description: The empty set is not a signed real. |
| Ref | Expression |
|---|---|
| 0nsr |
     |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dmenr 5240 |
. . 3
       | |
| 2 | 1 | 0nelqs 4359 |
. 2
 |
| 3 | df-nr 5232 |
. . 3
| |
| 4 | 3 | eleq2i 1585 |
. 2
 |
| 5 | 2, 4 | mtbir 199 |
1
|
| Colors of variables: wff set class |
| Syntax hints: wn 2
wcel 999
c0 2331
cxp 3225
cqs 4318
cnp 5050
cer 5057
cnr 5058 |
| This theorem is referenced by: dmaddsr 5259 dmmulsr 5260 addasssr 5262 mulasssr 5264 distrsr 5265 ltasr 5274 recexsrlem 5277 supsrlem1 5290 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1003 ax-gen 1004 ax-8 1005 ax-9 1006 ax-10 1007 ax-11 1008 ax-12 1009 ax-13 1010 ax-14 1011 ax-17 1012 ax-4 1014 ax-5o 1016 ax-6o 1019 ax-9o 1164 ax-10o 1182 ax-16 1252 ax-11o 1260 ax-ext 1504 ax-rep 2748 ax-sep 2758 ax-nul 2765 ax-pow 2798 ax-pr 2835 ax-un 2922 ax-inf2 4687 |
| This theorem depends on definitions: df-bi 154 df-or 231 df-an 232 df-3or 788 df-3an 789 df-ex 1022 df-sb 1214 df-eu 1424 df-mo 1425 df-clab 1510 df-cleq 1515 df-clel 1518 df-ne 1634 df-ral 1696 df-rex 1697 df-reu 1698 df-rab 1699 df-v 1859 df-sbc 1989 df-csb 2052 df-dif 2100 df-un 2101 df-in 2102 df-ss 2104 df-nul 2332 df-if 2414 df-pw 2454 df-sn 2464 df-pr 2465 df-tp 2467 df-op 2468 df-uni 2558 df-int 2588 df-iun 2622 df-br 2675 df-opab 2722 df-tr 2736 df-eprel 2888 df-id 2891 df-po 2896 df-so 2906 df-fr 2974 df-we 2991 df-ord 3008 df-on 3009 df-lim 3010 df-suc 3011 df-om 3189 df-xp 3241 df-rel 3242 df-cnv 3243 df-co 3244 df-dm 3245 df-rn 3246 df-res 3247 df-ima 3248 df-fun 3249 df-fn 3250 df-f 3251 df-fv 3255 df-rdg 3990 df-opr 4023 df-oprab 4024 df-1st 4137 df-2nd 4138 df-1o 4191 df-oadd 4193 df-omul 4194 df-er 4319 df-ec 4321 df-qs 4324 df-ni 5065 df-pli 5066 df-mi 5067 df-plpq 5100 df-enq 5102 df-nq 5103 df-plq 5104 df-plp 5153 df-enr 5231 df-nr 5232 |