Theorem isanmbfm 32856

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 7393	. 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM
2		isanmbfm.1	. 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇))
3	1, 2	sselid 3942	1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM)

Syntax hints:   → wi 4   ∈ wcel 2106  ∪ cuni 4865  ran crn 5634  (class class class)co 7357  MblFnMcmbfm 32848

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2707  ax-sep 5256  ax-nul 5263  ax-pr 5384

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2538  df-eu 2567  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2944  df-ral 3065  df-rex 3074  df-rab 3408  df-v 3447  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4283  df-if 4487  df-sn 4587  df-pr 4589  df-op 4593  df-uni 4866  df-br 5106  df-opab 5168  df-cnv 5641  df-dm 5643  df-rn 5644  df-iota 6448  df-fv 6504  df-ov 7360

This theorem is referenced by:  mbfmbfmOLD  32857  mbfmbfm  32858  orvcval4  33060