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| Mirrors > Home > MPE Home > Th. List > Mathboxes > mbfmbfmOLD | Structured version Visualization version GIF version | ||
| Description: A measurable function to a Borel Set is measurable. (Contributed by Thierry Arnoux, 24-Jan-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| mbfmbfmOLD.1 | ⊢ (𝜑 → 𝑀 ∈ ∪ ran measures) |
| mbfmbfmOLD.2 | ⊢ (𝜑 → 𝐽 ∈ Top) |
| mbfmbfmOLD.3 | ⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽))) |
| Ref | Expression |
|---|---|
| mbfmbfmOLD | ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mbfmbfmOLD.3 | . 2 ⊢ (𝜑 → 𝐹 ∈ (dom 𝑀MblFnM(sigaGen‘𝐽))) | |
| 2 | 1 | isanmbfm 34553 | 1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∈ wcel 2142 ∪ cuni 4865 dom cdm 5647 ran crn 5648 ‘cfv 6521 (class class class)co 7396 Topctop 22953 sigaGencsigagen 34435 measurescmeas 34492 MblFnMcmbfm 34546 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1815 ax-4 1829 ax-5 1930 ax-6 1987 ax-7 2028 ax-8 2144 ax-9 2152 ax-10 2175 ax-12 2212 ax-ext 2734 ax-sep 5246 ax-nul 5256 ax-pr 5390 |
| This theorem depends on definitions: df-bi 209 df-an 400 df-or 859 df-3an 1100 df-tru 1563 df-fal 1573 df-ex 1800 df-nf 1804 df-sb 2091 df-mo 2566 df-eu 2596 df-clab 2741 df-cleq 2754 df-clel 2837 df-ne 2958 df-rab 3415 df-v 3456 df-dif 3907 df-un 3909 df-in 3911 df-ss 3921 df-nul 4286 df-if 4481 df-sn 4583 df-pr 4585 df-op 4589 df-uni 4866 df-br 5101 df-opab 5163 df-cnv 5655 df-dm 5657 df-rn 5658 df-iota 6477 df-fv 6529 df-ov 7399 |
| This theorem is referenced by: (None) |
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