Theorem mbfmbfmOLD 34801

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 34800	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  ∪ cuni 4867  dom cdm 5655  ran crn 5656  ‘cfv 6535  (class class class)co 7416  Topctop 23150  sigaGencsigagen 34682  measurescmeas 34739  MblFnMcmbfm 34793

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-10 2178  ax-12 2213  ax-ext 2732  ax-sep 5251  ax-nul 5263  ax-pr 5398

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2100  df-mo 2564  df-eu 2594  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-rab 3413  df-v 3452  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-opab 5168  df-cnv 5663  df-dm 5665  df-rn 5666  df-iota 6491  df-fv 6543  df-ov 7419

This theorem is used by: (None)