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Theorem mbfmbfmOLD 34555
Description: A measurable function to a Borel Set is measurable. (Contributed by Thierry Arnoux, 24-Jan-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
mbfmbfmOLD.1 (𝜑𝑀 ran measures)
mbfmbfmOLD.2 (𝜑𝐽 ∈ Top)
mbfmbfmOLD.3 (𝜑𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))
Assertion
Ref Expression
mbfmbfmOLD (𝜑𝐹 ran MblFnM)

Proof of Theorem mbfmbfmOLD
StepHypRef Expression
1 mbfmbfmOLD.3 . 2 (𝜑𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))
21isanmbfm 34554 1 (𝜑𝐹 ran MblFnM)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2143   cuni 4866  dom cdm 5648  ran crn 5649  cfv 6522  (class class class)co 7397  Topctop 22954  sigaGencsigagen 34436  measurescmeas 34493  MblFnMcmbfm 34547
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-10 2176  ax-12 2213  ax-ext 2735  ax-sep 5247  ax-nul 5257  ax-pr 5391
This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1564  df-fal 1574  df-ex 1801  df-nf 1805  df-sb 2092  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-rab 3416  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5102  df-opab 5164  df-cnv 5656  df-dm 5658  df-rn 5659  df-iota 6478  df-fv 6530  df-ov 7400
This theorem is referenced by: (None)
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