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Theorem salunid 41314
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 41287 . 2 (𝑆 ∈ SAlg → 𝑆𝑆)
31, 2syl 17 1 (𝜑 𝑆𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2157   cuni 4628  SAlgcsalg 41271
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-rab 3098  df-v 3387  df-dif 3772  df-in 3776  df-ss 3783  df-nul 4116  df-pw 4351  df-uni 4629  df-salg 41272
This theorem is referenced by:  subsaluni  41321  smfpimltxr  41702  smfconst  41704  smfpimgtxr  41734
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