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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > salunid | Structured version Visualization version GIF version |
Description: A set is an element of any sigma-algebra on it. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
salunid.1 | ⊢ (𝜑 → 𝑆 ∈ SAlg) |
Ref | Expression |
---|---|
salunid | ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | salunid.1 | . 2 ⊢ (𝜑 → 𝑆 ∈ SAlg) | |
2 | saluni 44652 | . 2 ⊢ (𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2107 ∪ cuni 4866 SAlgcsalg 44635 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-ral 3062 df-rab 3407 df-v 3446 df-dif 3914 df-in 3918 df-ss 3928 df-nul 4284 df-pw 4563 df-uni 4867 df-salg 44636 |
This theorem is referenced by: subsaluni 44687 smfconst 45076 |
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