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Related theorems Unicode version |
| Description: Membership in positive reals. |
| Ref | Expression |
|---|---|
| elnp |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elisset 2299 |
. 2
| |
| 2 | pssss 2705 |
. . . 4
| |
| 3 | nqex 6201 |
. . . . 5
| |
| 4 | 3 | ssex 3455 |
. . . 4
|
| 5 | 2, 4 | syl 12 |
. . 3
|
| 6 | 5 | ad2antlr 441 |
. 2
|
| 7 | psseq2 2698 |
. . . . 5
| |
| 8 | psseq1 2697 |
. . . . 5
| |
| 9 | 7, 8 | anbi12d 690 |
. . . 4
|
| 10 | eleq2 1958 |
. . . . . . . 8
| |
| 11 | 10 | imbi2d 674 |
. . . . . . 7
|
| 12 | 11 | albidv 1656 |
. . . . . 6
|
| 13 | rexeq 2267 |
. . . . . 6
| |
| 14 | 12, 13 | anbi12d 690 |
. . . . 5
|
| 15 | 14 | raleqbi1dv 2271 |
. . . 4
|
| 16 | 9, 15 | anbi12d 690 |
. . 3
|
| 17 | df-np 6238 |
. . 3
| |
| 18 | 16, 17 | elab2g 2406 |
. 2
|
| 19 | 1, 6, 18 | pm5.21nii 743 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: prn0 6245 prpssnq 6246 prcdpq 6249 prnmax 6251 genpcl 6263 1pr 6269 ltexprlem5 6298 reclem2pr 6309 suplem1pr 6313 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1304 ax-gen 1305 ax-8 1306 ax-9 1307 ax-10 1308 ax-11 1309 ax-12 1310 ax-13 1311 ax-14 1312 ax-17 1317 ax-4 1319 ax-5o 1321 ax-6o 1324 ax-9o 1481 ax-10o 1500 ax-16 1580 ax-11o 1588 ax-ext 1865 ax-rep 3428 ax-sep 3438 ax-nul 3445 ax-pow 3481 ax-pr 3524 ax-un 3790 ax-inf2 5731 |
| This theorem depends on definitions: df-bi 164 df-or 241 df-an 242 df-3or 859 df-3an 860 df-ex 1327 df-sb 1536 df-eu 1775 df-mo 1776 df-clab 1872 df-cleq 1877 df-clel 1880 df-ne 2019 df-ral 2109 df-rex 2110 df-rab 2112 df-v 2294 df-dif 2597 df-un 2600 df-in 2603 df-ss 2605 df-pss 2607 df-nul 2876 df-if 2983 df-pw 3035 df-sn 3049 df-pr 3050 df-tp 3052 df-op 3053 df-uni 3178 df-br 3339 df-opab 3396 df-tr 3412 df-eprel 3583 df-id 3586 df-po 3591 df-so 3604 df-fr 3625 df-we 3644 df-ord 3660 df-on 3661 df-lim 3662 df-suc 3663 df-om 3950 df-xp 4000 df-rel 4001 df-cnv 4002 df-co 4003 df-dm 4004 df-rn 4005 df-res 4006 df-ima 4007 df-fun 4008 df-fn 4009 df-qs 5323 df-ni 6152 df-nq 6190 df-np 6238 |