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| Mirrors > Home > MPE Home > Th. List > Mathboxes > isanmbfmOLD | Structured version Visualization version GIF version | ||
| Description: Obsolete version of isanmbfm 34258 as of 13-Jan-2025. (Contributed by Thierry Arnoux, 30-Jan-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| mbfmf.1 | ⊢ (𝜑 → 𝑆 ∈ ∪ ran sigAlgebra) |
| mbfmf.2 | ⊢ (𝜑 → 𝑇 ∈ ∪ ran sigAlgebra) |
| mbfmf.3 | ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇)) |
| Ref | Expression |
|---|---|
| isanmbfmOLD | ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ovssunirn 7467 | . 2 ⊢ (𝑆MblFnM𝑇) ⊆ ∪ ran MblFnM | |
| 2 | mbfmf.3 | . 2 ⊢ (𝜑 → 𝐹 ∈ (𝑆MblFnM𝑇)) | |
| 3 | 1, 2 | sselid 3981 | 1 ⊢ (𝜑 → 𝐹 ∈ ∪ ran MblFnM) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∈ wcel 2108 ∪ cuni 4907 ran crn 5686 (class class class)co 7431 sigAlgebracsiga 34109 MblFnMcmbfm 34250 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-opab 5206 df-cnv 5693 df-dm 5695 df-rn 5696 df-iota 6514 df-fv 6569 df-ov 7434 |
| This theorem is referenced by: (None) |
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