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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > isanmbfm | Structured version Visualization version GIF version |
Description: The predicate to be a measurable function. (Contributed by Thierry Arnoux, 30-Jan-2017.) Remove hypotheses. (Revised by SN, 13-Jan-2025.) |
Ref | Expression |
---|---|
isanmbfm.1 | ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇)) |
Ref | Expression |
---|---|
isanmbfm | ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovssunirn 7456 | . 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM | |
2 | isanmbfm.1 | . 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇)) | |
3 | 1, 2 | sselid 3978 | 1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2099 ∪ cuni 4908 ran crn 5679 (class class class)co 7420 MblFnMcmbfm 33868 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pr 5429 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-ne 2938 df-ral 3059 df-rex 3068 df-rab 3430 df-v 3473 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-br 5149 df-opab 5211 df-cnv 5686 df-dm 5688 df-rn 5689 df-iota 6500 df-fv 6556 df-ov 7423 |
This theorem is referenced by: mbfmbfmOLD 33877 mbfmbfm 33878 orvcval4 34080 |
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