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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mbfmbfm | Structured version Visualization version GIF version |
Description: A measurable function to a Borel Set is measurable. (Contributed by Thierry Arnoux, 24-Jan-2017.) Remove hypotheses. (Revised by SN, 13-Jan-2025.) |
Ref | Expression |
---|---|
mbfmbfm.1 | ⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽))) |
Ref | Expression |
---|---|
mbfmbfm | ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mbfmbfm.1 | . 2 ⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽))) | |
2 | 1 | isanmbfm 34103 | 1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2099 ∪ cuni 4905 dom cdm 5674 ran crn 5675 ‘cfv 6546 (class class class)co 7416 sigaGencsigagen 33984 MblFnMcmbfm 34095 |
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 2697 ax-sep 5296 ax-nul 5303 ax-pr 5425 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2529 df-eu 2558 df-clab 2704 df-cleq 2718 df-clel 2803 df-ne 2931 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3464 df-dif 3949 df-un 3951 df-ss 3963 df-nul 4323 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4906 df-br 5146 df-opab 5208 df-cnv 5682 df-dm 5684 df-rn 5685 df-iota 6498 df-fv 6554 df-ov 7419 |
This theorem is referenced by: (None) |
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