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Theorem isanmbfm 33909
Description: The predicate to be a measurable function. (Contributed by Thierry Arnoux, 30-Jan-2017.) Remove hypotheses. (Revised by SN, 13-Jan-2025.)
Hypothesis
Ref Expression
isanmbfm.1 (𝜑𝐹 ∈ (𝑆MblFnM𝑇))
Assertion
Ref Expression
isanmbfm (𝜑𝐹 ran MblFnM)

Proof of Theorem isanmbfm
StepHypRef Expression
1 ovssunirn 7462 . 2 (𝑆MblFnM𝑇) ⊆ ran MblFnM
2 isanmbfm.1 . 2 (𝜑𝐹 ∈ (𝑆MblFnM𝑇))
31, 2sselid 3980 1 (𝜑𝐹 ran MblFnM)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098   cuni 4912  ran crn 5683  (class class class)co 7426  MblFnMcmbfm 33901
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-opab 5215  df-cnv 5690  df-dm 5692  df-rn 5693  df-iota 6505  df-fv 6561  df-ov 7429
This theorem is referenced by:  mbfmbfmOLD  33910  mbfmbfm  33911  orvcval4  34113
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