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Mirrors > Home > ILE Home > Th. List > eluz | Unicode version |
Description: Membership in an upper set of integers. (Contributed by NM, 2-Oct-2005.) |
Ref | Expression |
---|---|
eluz |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluz1 9354 |
. 2
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2 | 1 | baibd 909 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-cnex 7735 ax-resscn 7736 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-ov 5785 df-neg 7960 df-z 9079 df-uz 9351 |
This theorem is referenced by: uzneg 9368 uztric 9371 uzm1 9380 eluzdc 9431 fzn 9853 fzsplit2 9861 fznn 9900 uzsplit 9903 elfz2nn0 9923 fzouzsplit 9987 exfzdc 10048 fzfig 10234 faclbnd 10519 seq3coll 10617 cvg1nlemcau 10788 cvg1nlemres 10789 summodclem2a 11182 fsum0diaglem 11241 mertenslemi1 11336 prodmodclem2a 11377 zsupcllemstep 11674 zsupcl 11676 infssuzex 11678 uzdcinzz 13176 |
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