Theorem esumex

Description: An extended sum is a set by definition. (Contributed by Thierry Arnoux, 5-Sep-2017)

	Ref	Expression
Assertion	esumex	⊢ Σ* 𝑘 ∈ 𝐴 𝐵 ∈ V

Proof

Step	Hyp	Ref	Expression
1		df-esum	⊢ Σ* 𝑘 ∈ 𝐴 𝐵 = ∪ ( ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) tsums ( 𝑘 ∈ 𝐴 ↦ 𝐵 ) )
2		ovex	⊢ ( ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) tsums ( 𝑘 ∈ 𝐴 ↦ 𝐵 ) ) ∈ V
3	2	uniex	⊢ ∪ ( ( ℝ*𝑠 ↾s ( 0 [,] +∞ ) ) tsums ( 𝑘 ∈ 𝐴 ↦ 𝐵 ) ) ∈ V
4	1 3	eqeltri	⊢ Σ* 𝑘 ∈ 𝐴 𝐵 ∈ V