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Theorem elrnsiga 28944
Description: Dropping the base information off a sigma-algebra. (Contributed by Thierry Arnoux, 13-Feb-2017.)
Assertion
Ref Expression
elrnsiga  |-  ( S  e.  (sigAlgebra `  O )  ->  S  e.  U. ran sigAlgebra )

Proof of Theorem elrnsiga
StepHypRef Expression
1 fvssunirn 5901 . 2  |-  (sigAlgebra `  O
)  C_  U. ran sigAlgebra
21sseli 3460 1  |-  ( S  e.  (sigAlgebra `  O )  ->  S  e.  U. ran sigAlgebra )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1868   U.cuni 4216   ran crn 4851   ` cfv 5598  sigAlgebracsiga 28925
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-8 1870  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4552  ax-pow 4599  ax-pr 4657
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2269  df-mo 2270  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-ral 2780  df-rex 2781  df-rab 2784  df-v 3083  df-sbc 3300  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-uni 4217  df-br 4421  df-opab 4480  df-cnv 4858  df-dm 4860  df-rn 4861  df-iota 5562  df-fv 5606
This theorem is referenced by:  sgsiga  28960  sigapisys  28973  sigaldsys  28977  brsiga  29001  sxsiga  29009  measinb2  29041  pwcntmeas  29045  ddemeas  29055  cnmbfm  29081  elmbfmvol2  29085  mbfmcnt  29086  br2base  29087  dya2iocbrsiga  29093  dya2icobrsiga  29094  sxbrsiga  29108  omsmeas  29151  omsmeasOLD  29152  isrrvv  29272  rrvadd  29281  rrvmulc  29282  dstrvprob  29300
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