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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fzo 10129 |
. 2
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2 | 1 | elmpocl2 6065 |
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-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-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 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-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-iota 5174 df-fun 5214 df-fv 5220 df-ov 5872 df-oprab 5873 df-mpo 5874 df-fzo 10129 |
This theorem is referenced by: elfzoelz 10133 elfzo2 10136 elfzole1 10141 elfzolt2 10142 elfzolt3 10143 elfzolt2b 10144 elfzolt3b 10145 fzonel 10146 elfzouz2 10147 fzonnsub 10155 fzoss1 10157 fzospliti 10162 fzodisj 10164 fzoaddel 10178 fzosubel 10180 fzoend 10208 ssfzo12 10210 fzofzp1 10213 peano2fzor 10218 fzostep1 10223 iseqf1olemqk 10480 fzomaxdiflem 11105 fzo0dvdseq 11846 fzocongeq 11847 addmodlteqALT 11848 |
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