Theorem isanmbfm 34655

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	⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))

Assertion

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

Proof of Theorem isanmbfm

Step	Hyp	Ref	Expression
1		ovssunirn 7448	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		isanmbfm.1	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3934	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  ∪ cuni 4871  ran crn 5661  (class class class)co 7412  MblFnMcmbfm 34648

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-10 2175  ax-12 2212  ax-ext 2734  ax-sep 5256  ax-nul 5268  ax-pr 5403

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1104  df-tru 1572  df-fal 1582  df-ex 1809  df-nf 1813  df-sb 2096  df-mo 2566  df-eu 2596  df-clab 2741  df-cleq 2754  df-clel 2837  df-ne 2958  df-rab 3416  df-v 3456  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-uni 4872  df-br 5109  df-opab 5173  df-cnv 5668  df-dm 5670  df-rn 5671  df-iota 6492  df-fv 6544  df-ov 7415

This theorem is used by:  mbfmbfmOLD  34656  mbfmbfm  34657  orvcval4  34860