Theorem salunid 46796

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 46768	. 2 ⊢ (𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆)
3	1, 2	syl 17	1 ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆)

Syntax hints:   → wi 4   ∈ wcel 2119  ∪ cuni 4838  SAlgcsalg 46751

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-ral 3054  df-rab 3392  df-v 3433  df-dif 3886  df-ss 3900  df-nul 4262  df-pw 4531  df-uni 4839  df-salg 46752

This theorem is referenced by:  subsaluni  46803  smfconst  47192