Theorem salunid 46337

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 46309	. 2 ⊢ (𝑆 ∈ SAlg → ∪ 𝑆 ∈ 𝑆)
3	1, 2	syl 17	1 ⊢ (𝜑 → ∪ 𝑆 ∈ 𝑆)

Syntax hints:   → wi 4   ∈ wcel 2108  ∪ cuni 4915  SAlgcsalg 46292

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rab 3437  df-v 3483  df-dif 3969  df-ss 3983  df-nul 4343  df-pw 4610  df-uni 4916  df-salg 46293

This theorem is referenced by:  subsaluni  46344  smfconst  46733