Theorem salunid 46959

Description: A set is an element of any sigma-algebra on it. (Contributed by Glauco Siliprandi, 26-Jun-2021.)

Hypothesis

Ref	Expression
salunid.1	⊢ (𝜑 → 𝑆 ∈ SAlg)

Assertion

Ref	Expression
salunid	⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆)

Proof of Theorem salunid

Step	Hyp	Ref	Expression
1		salunid.1	. 2 ⊢ (𝜑 → 𝑆 ∈ SAlg)
2		saluni 46931	. 2 ⊢ (𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆)
3	1, 2	syl 18	1 ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆)

Syntax hints:   → wi 4   ∈ wcel 2149  ∪ cuni 4876  SAlgcsalg 46914

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ral 3086  df-rab 3424  df-v 3465  df-dif 3916  df-ss 3930  df-nul 4295  df-pw 4569  df-uni 4877  df-salg 46915

This theorem is referenced by:  subsaluni  46966  smfconst  47355