![]() |
Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > elrnsiga | Structured version Visualization version GIF version |
Description: Dropping the base information off a sigma-algebra. (Contributed by Thierry Arnoux, 13-Feb-2017.) |
Ref | Expression |
---|---|
elrnsiga | ⊢ (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ∈ ∪ ran sigAlgebra) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvssunirn 6674 | . 2 ⊢ (sigAlgebra‘𝑂) ⊆ ∪ ran sigAlgebra | |
2 | 1 | sseli 3911 | 1 ⊢ (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ∈ ∪ ran sigAlgebra) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2111 ∪ cuni 4800 ran crn 5520 ‘cfv 6324 sigAlgebracsiga 31477 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pow 5231 ax-pr 5295 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-ral 3111 df-rex 3112 df-v 3443 df-sbc 3721 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-uni 4801 df-br 5031 df-opab 5093 df-cnv 5527 df-dm 5529 df-rn 5530 df-iota 6283 df-fv 6332 |
This theorem is referenced by: sgsiga 31511 sigapisys 31524 sigaldsys 31528 brsiga 31552 sxsiga 31560 measinb2 31592 pwcntmeas 31596 ddemeas 31605 cnmbfm 31631 elmbfmvol2 31635 mbfmcnt 31636 br2base 31637 dya2iocbrsiga 31643 dya2icobrsiga 31644 sxbrsiga 31658 omsmeas 31691 isrrvv 31811 rrvadd 31820 rrvmulc 31821 dstrvprob 31839 |
Copyright terms: Public domain | W3C validator |