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Theorem mbfmbfm 34105
Description: A measurable function to a Borel Set is measurable. (Contributed by Thierry Arnoux, 24-Jan-2017.) Remove hypotheses. (Revised by SN, 13-Jan-2025.)
Hypothesis
Ref Expression
mbfmbfm.1 (𝜑𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))
Assertion
Ref Expression
mbfmbfm (𝜑𝐹 ran MblFnM)

Proof of Theorem mbfmbfm
StepHypRef Expression
1 mbfmbfm.1 . 2 (𝜑𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))
21isanmbfm 34103 1 (𝜑𝐹 ran MblFnM)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099   cuni 4905  dom cdm 5674  ran crn 5675  cfv 6546  (class class class)co 7416  sigaGencsigagen 33984  MblFnMcmbfm 34095
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2697  ax-sep 5296  ax-nul 5303  ax-pr 5425
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2529  df-eu 2558  df-clab 2704  df-cleq 2718  df-clel 2803  df-ne 2931  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3464  df-dif 3949  df-un 3951  df-ss 3963  df-nul 4323  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4906  df-br 5146  df-opab 5208  df-cnv 5682  df-dm 5684  df-rn 5685  df-iota 6498  df-fv 6554  df-ov 7419
This theorem is referenced by: (None)
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