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	⊢ (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 46248	. 2 ⊢ (𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆)
3	1, 2	syl 17	1 ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆)

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