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Theorem salunid 46276
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 46248 . 2 (𝑆 ∈ SAlg → 𝑆𝑆)
31, 2syl 17 1 (𝜑 𝑆𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108   cuni 4931  SAlgcsalg 46231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ral 3068  df-rab 3444  df-v 3490  df-dif 3979  df-ss 3993  df-nul 4353  df-pw 4624  df-uni 4932  df-salg 46232
This theorem is referenced by:  subsaluni  46283  smfconst  46672
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