Users' Mathboxes Mathbox for Thierry Arnoux < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  elrnsiga Structured version   Visualization version   GIF version

Theorem elrnsiga 34107
Description: Dropping the base information off a sigma-algebra. (Contributed by Thierry Arnoux, 13-Feb-2017.)
Assertion
Ref Expression
elrnsiga (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ran sigAlgebra)

Proof of Theorem elrnsiga
StepHypRef Expression
1 fvssunirn 6940 . 2 (sigAlgebra‘𝑂) ⊆ ran sigAlgebra
21sseli 3991 1 (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ran sigAlgebra)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106   cuni 4912  ran crn 5690  cfv 6563  sigAlgebracsiga 34089
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-cnv 5697  df-dm 5699  df-rn 5700  df-iota 6516  df-fv 6571
This theorem is referenced by:  sgsiga  34123  sigapisys  34136  sigaldsys  34140  brsiga  34164  sxsiga  34172  measinb2  34204  pwcntmeas  34208  ddemeas  34217  cnmbfm  34245  elmbfmvol2  34249  mbfmcnt  34250  br2base  34251  dya2iocbrsiga  34257  dya2icobrsiga  34258  sxbrsiga  34272  omsmeas  34305  isrrvv  34425  rrvadd  34434  rrvmulc  34435  dstrvprob  34453
  Copyright terms: Public domain W3C validator