Metamath Proof Explorer


Theorem salunid

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

Ref Expression
Hypothesis salunid.1 ⊢ φ → S ∈ SAlg
Assertion salunid ⊢ φ → ⋃ S ∈ S

Proof

Step Hyp Ref Expression
1 salunid.1 ⊢ φ → S ∈ SAlg
2 saluni ⊢ S ∈ SAlg → ⋃ S ∈ S
3 1 2 syl ⊢ φ → ⋃ S ∈ S