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 42629 | . 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 2114 ∪ cuni 4838 SAlgcsalg 42613 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rab 3147 df-v 3496 df-dif 3939 df-in 3943 df-ss 3952 df-nul 4292 df-pw 4541 df-uni 4839 df-salg 42614 |
This theorem is referenced by: subsaluni 42663 smfpimltxr 43044 smfconst 43046 smfpimgtxr 43076 |
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