Metamath Proof Explorer


Theorem fveere

Description: The function value of a point is a real. (Contributed by Scott Fenton, 10-Jun-2013)

Ref Expression
Assertion fveere ( ( 𝐴 ∈ ( 𝔼 ‘ 𝑁 ) ∧ 𝐼 ∈ ( 1 ... 𝑁 ) ) → ( 𝐴𝐼 ) ∈ ℝ )

Proof

Step Hyp Ref Expression
1 eleei ( 𝐴 ∈ ( 𝔼 ‘ 𝑁 ) → 𝐴 : ( 1 ... 𝑁 ) ⟶ ℝ )
2 1 ffvelrnda ( ( 𝐴 ∈ ( 𝔼 ‘ 𝑁 ) ∧ 𝐼 ∈ ( 1 ... 𝑁 ) ) → ( 𝐴𝐼 ) ∈ ℝ )