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Theorem elrnsiga 32765
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 6880 . 2 (sigAlgebra‘𝑂) ⊆ ran sigAlgebra
21sseli 3945 1 (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ran sigAlgebra)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107   cuni 4870  ran crn 5639  cfv 6501  sigAlgebracsiga 32747
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708  ax-sep 5261  ax-nul 5268  ax-pr 5389
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-ral 3066  df-rex 3075  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-opab 5173  df-cnv 5646  df-dm 5648  df-rn 5649  df-iota 6453  df-fv 6509
This theorem is referenced by:  sgsiga  32781  sigapisys  32794  sigaldsys  32798  brsiga  32822  sxsiga  32830  measinb2  32862  pwcntmeas  32866  ddemeas  32875  cnmbfm  32903  elmbfmvol2  32907  mbfmcnt  32908  br2base  32909  dya2iocbrsiga  32915  dya2icobrsiga  32916  sxbrsiga  32930  omsmeas  32963  isrrvv  33083  rrvadd  33092  rrvmulc  33093  dstrvprob  33111
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