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Related theorems Unicode version |
| Description: Membership in positive reals. |
| Ref | Expression |
|---|---|
| elnp |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elisset 1855 |
. 2
| |
| 2 | pssss 2187 |
. . . 4
| |
| 3 | nqex 5138 |
. . . . 5
| |
| 4 | 3 | ssex 2770 |
. . . 4
|
| 5 | 2, 4 | syl 10 |
. . 3
|
| 6 | 5 | ad2antlr 405 |
. 2
|
| 7 | psseq2 2180 |
. . . . 5
| |
| 8 | psseq1 2179 |
. . . . 5
| |
| 9 | 7, 8 | anbi12d 630 |
. . . 4
|
| 10 | eleq2 1572 |
. . . . . . . 8
| |
| 11 | 10 | imbi2d 614 |
. . . . . . 7
|
| 12 | 11 | albidv 1311 |
. . . . . 6
|
| 13 | rexeq1 1825 |
. . . . . 6
| |
| 14 | 12, 13 | anbi12d 630 |
. . . . 5
|
| 15 | 14 | raleqd 1829 |
. . . 4
|
| 16 | 9, 15 | anbi12d 630 |
. . 3
|
| 17 | df-np 5175 |
. . 3
| |
| 18 | 16, 17 | elab2g 1938 |
. 2
|
| 19 | 1, 6, 18 | pm5.21nii 682 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: prn0 5182 prpssnq 5183 prcdpq 5186 prnmax 5188 genpcl 5200 1pr 5206 ltexprlem5 5235 reclem2pr 5246 suplem1pr 5250 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 994 ax-gen 995 ax-8 996 ax-9 997 ax-10 998 ax-11 999 ax-12 1000 ax-13 1001 ax-14 1002 ax-17 1003 ax-4 1005 ax-5o 1007 ax-6o 1010 ax-9o 1155 ax-10o 1173 ax-16 1243 ax-11o 1251 ax-ext 1494 ax-rep 2744 ax-sep 2754 ax-nul 2761 ax-pow 2794 ax-pr 2832 ax-un 2920 ax-inf2 4711 |
| This theorem depends on definitions: df-bi 145 df-or 222 df-an 223 df-3or 779 df-3an 780 df-ex 1013 df-sb 1205 df-eu 1415 df-mo 1416 df-clab 1500 df-cleq 1505 df-clel 1508 df-ne 1624 df-ral 1687 df-rex 1688 df-v 1850 df-dif 2093 df-un 2094 df-in 2095 df-ss 2097 df-pss 2099 df-nul 2325 df-if 2407 df-pw 2447 df-sn 2457 df-pr 2458 df-tp 2460 df-op 2461 df-uni 2552 df-br 2670 df-opab 2718 df-tr 2732 df-eprel 2886 df-id 2889 df-po 2894 df-so 2904 df-fr 2972 df-we 2989 df-ord 3006 df-on 3007 df-lim 3008 df-suc 3009 df-om 3193 df-xp 3239 df-rel 3240 df-cnv 3241 df-co 3242 df-dm 3243 df-rn 3244 df-res 3245 df-ima 3246 df-fun 3247 df-fn 3248 df-qs 4350 df-ni 5089 df-nq 5127 df-np 5175 |