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Theorem salunid 44680
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 44652 . 2 (𝑆 ∈ SAlg → 𝑆𝑆)
31, 2syl 17 1 (𝜑 𝑆𝑆)
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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