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Mirrors > Home > MPE Home > Th. List > icossxr | Structured version Visualization version Unicode version |
Description: A closed-below, open-above interval is a subset of the extended reals. (Contributed by FL, 29-May-2014.) (Revised by Mario Carneiro, 4-Jul-2014.) |
Ref | Expression |
---|---|
icossxr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ico 12181 | . 2 | |
2 | 1 | ixxssxr 12187 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wss 3574 (class class class)co 6650 cxr 10073 clt 10074 cle 10075 cico 12177 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-xr 10078 df-ico 12181 |
This theorem is referenced by: leordtvallem2 21015 leordtval2 21016 nmoffn 22515 nmofval 22518 nmogelb 22520 nmolb 22521 nmof 22523 icopnfhmeo 22742 elovolm 23243 ovolmge0 23245 ovolgelb 23248 ovollb2lem 23256 ovoliunlem1 23270 ovoliunlem2 23271 ovolscalem1 23281 ovolicc1 23284 ioombl1lem2 23327 ioombl1lem4 23329 uniioovol 23347 uniiccvol 23348 uniioombllem1 23349 uniioombllem2 23351 uniioombllem3 23353 uniioombllem6 23356 esumpfinvallem 30136 esummulc1 30143 esummulc2 30144 mblfinlem3 33448 mblfinlem4 33449 ismblfin 33450 itg2gt0cn 33465 xralrple2 39570 icoub 39752 liminflelimsuplem 40007 elhoi 40756 hoidmvlelem5 40813 ovnhoilem1 40815 ovnhoilem2 40816 ovnhoi 40817 |
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