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Theorem salunid 45622
Description: A set is an element of any sigma-algebra on it. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
salunid.1 (𝜑𝑆 ∈ SAlg)
Assertion
Ref Expression
salunid (𝜑 𝑆𝑆)

Proof of Theorem salunid
StepHypRef Expression
1 salunid.1 . 2 (𝜑𝑆 ∈ SAlg)
2 saluni 45594 . 2 (𝑆 ∈ SAlg → 𝑆𝑆)
31, 2syl 17 1 (𝜑 𝑆𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098   cuni 4902  SAlgcsalg 45577
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ral 3056  df-rab 3427  df-v 3470  df-dif 3946  df-in 3950  df-ss 3960  df-nul 4318  df-pw 4599  df-uni 4903  df-salg 45578
This theorem is referenced by:  subsaluni  45629  smfconst  46018
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