Metamath Proof Explorer


Theorem im1

Description: The imaginary part of one. (Contributed by Scott Fenton, 9-Jun-2006)

Ref Expression
Assertion im1 ⊢ ℑ ⁡ 1 = 0

Proof

Step Hyp Ref Expression
1 1re ⊢ 1 ∈ ℝ
2 reim0 ⊢ 1 ∈ ℝ → ℑ ⁡ 1 = 0
3 1 2 ax-mp ⊢ ℑ ⁡ 1 = 0