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