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Mirrors > Home > ILE Home > Th. List > eluznn | Unicode version |
Description: Membership in a positive
upper set of integers implies membership in
![]() |
Ref | Expression |
---|---|
eluznn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnuz 9566 |
. 2
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2 | 1 | uztrn2 9548 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-setind 4538 ax-cnex 7905 ax-resscn 7906 ax-1cn 7907 ax-1re 7908 ax-icn 7909 ax-addcl 7910 ax-addrcl 7911 ax-mulcl 7912 ax-addcom 7914 ax-addass 7916 ax-distr 7918 ax-i2m1 7919 ax-0lt1 7920 ax-0id 7922 ax-rnegex 7923 ax-cnre 7925 ax-pre-ltirr 7926 ax-pre-ltwlin 7927 ax-pre-lttrn 7928 ax-pre-ltadd 7930 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2741 df-sbc 2965 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-opab 4067 df-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-ima 4641 df-iota 5180 df-fun 5220 df-fn 5221 df-f 5222 df-fv 5226 df-riota 5834 df-ov 5881 df-oprab 5882 df-mpo 5883 df-pnf 7997 df-mnf 7998 df-xr 7999 df-ltxr 8000 df-le 8001 df-sub 8133 df-neg 8134 df-inn 8923 df-z 9257 df-uz 9532 |
This theorem is referenced by: elfzo1 10193 bcval5 10746 caucvgrelemcau 10992 caucvgre 10993 cvg1nlemcau 10996 cvg1nlemres 10997 resqrexlemcvg 11031 resqrexlemgt0 11032 resqrexlemglsq 11034 resqrexlemga 11035 climrecvg1n 11359 climcvg1nlem 11360 cvgratnnlemmn 11536 cvgratnnlemseq 11537 cvgratnnlemrate 11541 mertenslem2 11547 pcmpt2 12345 pcmptdvds 12346 strext 12567 mulgnndir 13022 lgsdilem2 14598 cvgcmp2nlemabs 14942 trilpolemisumle 14948 trilpolemeq1 14950 trilpolemlt1 14951 nconstwlpolemgt0 14974 |
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