Metamath Proof Explorer

Theorem im1

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

Ref Expression
Assertion im1 
|- ( Im ` 1 ) = 0

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 reim0 
 |-  ( 1 e. RR -> ( Im ` 1 ) = 0 )
3 1 2 ax-mp 
 |-  ( Im ` 1 ) = 0