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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 7440 | . 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM | |
2 | isanmbfm.1 | . 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇)) | |
3 | 1, 2 | sselid 3975 | 1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2098 ∪ cuni 4902 ran crn 5670 (class class class)co 7404 MblFnMcmbfm 33776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pr 5420 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2704 df-cleq 2718 df-clel 2804 df-ne 2935 df-ral 3056 df-rex 3065 df-rab 3427 df-v 3470 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5142 df-opab 5204 df-cnv 5677 df-dm 5679 df-rn 5680 df-iota 6488 df-fv 6544 df-ov 7407 |
This theorem is referenced by: mbfmbfmOLD 33785 mbfmbfm 33786 orvcval4 33988 |
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