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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > eliccre | Structured version Visualization version Unicode version |
Description: A member of a closed interval of reals is real. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
eliccre |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elicc2 11699 |
. . 3
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2 | 1 | biimp3a 1369 |
. 2
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3 | 2 | simp1d 1020 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 ax-cnex 9595 ax-resscn 9596 ax-pre-lttri 9613 ax-pre-lttrn 9614 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-po 4755 df-so 4756 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-er 7363 df-en 7570 df-dom 7571 df-sdom 7572 df-pnf 9677 df-mnf 9678 df-xr 9679 df-ltxr 9680 df-le 9681 df-icc 11642 |
This theorem is referenced by: iccshift 37619 iccsuble 37620 cncfiooiccre 37773 itgioocnicc 37854 iblcncfioo 37855 itgspltprt 37856 itgiccshift 37857 itgperiod 37858 fourierdlem43 38014 fourierdlem44 38015 fourierdlem73 38043 fourierdlem81 38051 fourierdlem82 38052 fourierdlem83 38053 fourierdlem84 38054 fourierdlem92 38062 fourierdlem93 38063 fourierdlem101 38071 fourierdlem103 38073 fourierdlem104 38074 fourierdlem107 38077 fourierdlem111 38081 |
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