![]() |
Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > unielsiga | Structured version Visualization version GIF version |
Description: A sigma-algebra contains its universe set. (Contributed by Thierry Arnoux, 13-Feb-2017.) (Shortened by Thierry Arnoux, 6-Jun-2017.) |
Ref | Expression |
---|---|
unielsiga | β’ (π β βͺ ran sigAlgebra β βͺ π β π) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sgon 33110 | . 2 β’ (π β βͺ ran sigAlgebra β π β (sigAlgebraββͺ π)) | |
2 | baselsiga 33101 | . 2 β’ (π β (sigAlgebraββͺ π) β βͺ π β π) | |
3 | 1, 2 | syl 17 | 1 β’ (π β βͺ ran sigAlgebra β βͺ π β π) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β wcel 2106 βͺ cuni 4907 ran crn 5676 βcfv 6540 sigAlgebracsiga 33094 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-iota 6492 df-fun 6542 df-fn 6543 df-fv 6548 df-siga 33095 |
This theorem is referenced by: mbfmcst 33246 1stmbfm 33247 2ndmbfm 33248 imambfm 33249 mbfmco 33251 br2base 33256 prob01 33400 probfinmeasb 33415 |
Copyright terms: Public domain | W3C validator |