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Theorem elrnsiga 34127
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 6939 . 2 (sigAlgebra‘𝑂) ⊆ ran sigAlgebra
21sseli 3979 1 (𝑆 ∈ (sigAlgebra‘𝑂) → 𝑆 ran sigAlgebra)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108   cuni 4907  ran crn 5686  cfv 6561  sigAlgebracsiga 34109
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-cnv 5693  df-dm 5695  df-rn 5696  df-iota 6514  df-fv 6569
This theorem is referenced by:  sgsiga  34143  sigapisys  34156  sigaldsys  34160  brsiga  34184  sxsiga  34192  measinb2  34224  pwcntmeas  34228  ddemeas  34237  cnmbfm  34265  elmbfmvol2  34269  mbfmcnt  34270  br2base  34271  dya2iocbrsiga  34277  dya2icobrsiga  34278  sxbrsiga  34292  omsmeas  34325  isrrvv  34445  rrvadd  34454  rrvmulc  34455  dstrvprob  34474
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