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Mirrors > Home > ILE Home > Th. List > elfzoel2 | Unicode version |
Description: Reverse closure for half-open integer sets. (Contributed by Stefan O'Rear, 14-Aug-2015.) |
Ref | Expression |
---|---|
elfzoel2 | ..^ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fzo 9000 | . 2 ..^ | |
2 | 1 | elmpt2cl2 5700 | 1 ..^ |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 (class class class)co 5512 c1 6890 cmin 7182 cz 8245 cfz 8874 ..^cfzo 8999 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 df-fzo 9000 |
This theorem is referenced by: elfzoelz 9004 elfzo2 9007 elfzole1 9011 elfzolt2 9012 elfzolt3 9013 elfzolt2b 9014 elfzolt3b 9015 fzonel 9016 elfzouz2 9017 fzonnsub 9025 fzoss1 9027 fzospliti 9032 fzodisj 9034 fzoaddel 9048 fzosubel 9050 fzoend 9078 ssfzo12 9080 fzofzp1 9083 peano2fzor 9088 fzostep1 9093 fzomaxdiflem 9708 |
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