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Metamath Proof Explorer

Theorem itgex

Description: An integral is a set. (Contributed by Mario Carneiro, 28-Jun-2014)

Ref Expression
Assertion itgex ⊢ ∫ A B dx ∈ V

Proof

Step Hyp Ref Expression
1 df-itg ⊢ ∫ A B dx = ∑ k = 0 3 i k ⁢ ∫ 2 ⁡ x ∈ ℝ ⟼ ⦋ ℜ ⁡ B i k / y⦌ if x ∈ A ∧ 0 ≤ y y 0
2 sumex ⊢ ∑ k = 0 3 i k ⁢ ∫ 2 ⁡ x ∈ ℝ ⟼ ⦋ ℜ ⁡ B i k / y⦌ if x ∈ A ∧ 0 ≤ y y 0 ∈ V
3 1 2 eqeltri ⊢ ∫ A B dx ∈ V