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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > measbase | Structured version Visualization version Unicode version |
Description: The base set of a measure is a sigma-algebra. (Contributed by Thierry Arnoux, 25-Dec-2016.) |
Ref | Expression |
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measbase |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfvdm 5891 |
. 2
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2 | vex 3048 |
. . . . 5
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3 | ovex 6318 |
. . . . 5
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4 | mapex 7478 |
. . . . 5
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5 | 2, 3, 4 | mp2an 678 |
. . . 4
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6 | simp1 1008 |
. . . . 5
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7 | 6 | ss2abi 3501 |
. . . 4
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8 | 5, 7 | ssexi 4548 |
. . 3
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9 | df-meas 29018 |
. . 3
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10 | 8, 9 | dmmpti 5707 |
. 2
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11 | 1, 10 | syl6eleq 2539 |
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 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 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-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 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-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-fv 5590 df-ov 6293 df-meas 29018 |
This theorem is referenced by: measfrge0 29025 measvnul 29028 measvun 29031 measxun2 29032 measun 29033 measvuni 29036 measssd 29037 measunl 29038 measiuns 29039 measiun 29040 meascnbl 29041 measinblem 29042 measinb 29043 measinb2 29045 measdivcstOLD 29046 measdivcst 29047 aean 29067 mbfmbfm 29080 domprobsiga 29244 prob01 29246 probfinmeasbOLD 29261 probfinmeasb 29262 probmeasb 29263 |
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