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Mirrors > Home > MPE Home > Th. List > iccgelb | Structured version Visualization version Unicode version |
Description: An element of a closed interval is more than or equal to its lower bound. (Contributed by Thierry Arnoux, 23-Dec-2016.) |
Ref | Expression |
---|---|
iccgelb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elicc1 12219 | . . . 4 | |
2 | 1 | biimpa 501 | . . 3 |
3 | 2 | simp2d 1074 | . 2 |
4 | 3 | 3impa 1259 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 class class class wbr 4653 (class class class)co 6650 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-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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-xr 10078 df-icc 12182 |
This theorem is referenced by: supicc 12320 ttgcontlem1 25765 xrge0infss 29525 xrge0addgt0 29691 xrge0adddir 29692 esumcst 30125 esumpinfval 30135 oms0 30359 probmeasb 30492 broucube 33443 areaquad 37802 lefldiveq 39505 xadd0ge 39536 xrge0nemnfd 39548 eliccelioc 39747 iccintsng 39749 ge0nemnf2 39755 eliccnelico 39756 eliccelicod 39757 ge0xrre 39758 inficc 39761 iccdificc 39766 iccgelbd 39770 cncfiooiccre 40108 iblspltprt 40189 itgioocnicc 40193 itgspltprt 40195 itgiccshift 40196 fourierdlem1 40325 fourierdlem20 40344 fourierdlem24 40348 fourierdlem25 40349 fourierdlem27 40351 fourierdlem43 40367 fourierdlem44 40368 fourierdlem50 40373 fourierdlem51 40374 fourierdlem52 40375 fourierdlem64 40387 fourierdlem73 40396 fourierdlem76 40399 fourierdlem81 40404 fourierdlem92 40415 fourierdlem102 40425 fourierdlem103 40426 fourierdlem104 40427 fourierdlem114 40437 rrxsnicc 40520 salgencntex 40561 fge0iccico 40587 gsumge0cl 40588 sge0sn 40596 sge0tsms 40597 sge0cl 40598 sge0ge0 40601 sge0fsum 40604 sge0pr 40611 sge0prle 40618 sge0p1 40631 sge0rernmpt 40639 meage0 40692 omessre 40724 omeiunltfirp 40733 carageniuncllem2 40736 omege0 40747 ovnlerp 40776 ovn0lem 40779 hoidmvlelem1 40809 hoidmvlelem2 40810 hoidmvlelem3 40811 |
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