Theorem mbfmbfmOLD 34289

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	⊢ (𝜑 → 𝑀 ∈ ∪ ran measures)
mbfmbfmOLD.2	⊢ (𝜑 → 𝐽 ∈ Top)
mbfmbfmOLD.3	⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))

Assertion

Ref	Expression
mbfmbfmOLD	⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Proof of Theorem mbfmbfmOLD

Step	Hyp	Ref	Expression
1		mbfmbfmOLD.3	. 2 ⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽)))
2	1	isanmbfm 34288	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2108  ∪ cuni 4883  dom cdm 5654  ran crn 5655  ‘cfv 6531  (class class class)co 7405  Topctop 22831  sigaGencsigagen 34169  measurescmeas 34226  MblFnMcmbfm 34280

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 2707  ax-sep 5266  ax-nul 5276  ax-pr 5402

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2727  df-clel 2809  df-ne 2933  df-ral 3052  df-rex 3061  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-opab 5182  df-cnv 5662  df-dm 5664  df-rn 5665  df-iota 6484  df-fv 6539  df-ov 7408

This theorem is referenced by: (None)