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Mirrors > Home > MPE Home > Th. List > iccss | Structured version Visualization version Unicode version |
Description: Condition for a closed interval to be a subset of another closed interval. (Contributed by Jeff Madsen, 2-Sep-2009.) (Revised by Mario Carneiro, 20-Feb-2015.) |
Ref | Expression |
---|---|
iccss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexr 10085 | . . 3 | |
2 | rexr 10085 | . . 3 | |
3 | 1, 2 | anim12i 590 | . 2 |
4 | df-icc 12182 | . . 3 | |
5 | xrletr 11989 | . . 3 | |
6 | xrletr 11989 | . . 3 | |
7 | 4, 4, 5, 6 | ixxss12 12195 | . 2 |
8 | 3, 7 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 wss 3574 class class class wbr 4653 (class class class)co 6650 cr 9935 cxr 10073 cle 10075 cicc 12178 |
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 ax-pre-lttri 10010 ax-pre-lttrn 10011 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-nel 2898 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-po 5035 df-so 5036 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-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 df-icc 12182 |
This theorem is referenced by: xrhmeo 22745 lebnumii 22765 pcoval1 22813 pcoval2 22816 ivthicc 23227 dyaddisjlem 23363 volsup2 23373 volcn 23374 mbfi1fseqlem5 23486 dvcvx 23783 dvfsumle 23784 dvfsumabs 23786 harmonicbnd3 24734 ppisval 24830 chtwordi 24882 ppiwordi 24888 chpub 24945 cvmliftlem2 31268 fourierdlem76 40399 fourierdlem103 40426 fourierdlem104 40427 fourierdlem107 40430 fourierdlem112 40435 salexct3 40560 salgensscntex 40562 |
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