Theorem opnssborel

Description: Open sets of a generalized real Euclidean space are Borel sets (notice that this theorem is even more general, because X is not required to be a set). (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypotheses	opnssborel.a	⊢ 𝐴 = ( TopOpen ‘ ( ℝ^ ‘ 𝑋 ) )
	opnssborel.b	⊢ 𝐵 = ( SalGen ‘ 𝐴 )
Assertion	opnssborel	⊢ 𝐴 ⊆ 𝐵

Proof

Step	Hyp	Ref	Expression
1		opnssborel.a	⊢ 𝐴 = ( TopOpen ‘ ( ℝ^ ‘ 𝑋 ) )
2		opnssborel.b	⊢ 𝐵 = ( SalGen ‘ 𝐴 )
3	1	fvexi	⊢ 𝐴 ∈ V
4	2	sssalgen	⊢ ( 𝐴 ∈ V → 𝐴 ⊆ 𝐵 )
5	3 4	ax-mp	⊢ 𝐴 ⊆ 𝐵