Theorem mbfmbfmOLD 34656

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 34655	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2143  ∪ cuni 4872  dom cdm 5661  ran crn 5662  ‘cfv 6536  (class class class)co 7410  Topctop 23059  sigaGencsigagen 34537  measurescmeas 34594  MblFnMcmbfm 34648

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-10 2176  ax-12 2213  ax-ext 2735  ax-sep 5257  ax-nul 5269  ax-pr 5404

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-nf 1814  df-sb 2097  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-opab 5174  df-cnv 5669  df-dm 5671  df-rn 5672  df-iota 6492  df-fv 6544  df-ov 7413

This theorem is used by: (None)