Metamath Proof Explorer

Theorem reim0d

Description: The imaginary part of a real number is 0. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis crred.1 
|- ( ph -> A e. RR )
Assertion reim0d 
|- ( ph -> ( Im ` A ) = 0 )

Proof

Step Hyp Ref Expression
1 crred.1 
 |-  ( ph -> A e. RR )
2 reim0 
 |-  ( A e. RR -> ( Im ` A ) = 0 )
3 1 2 syl 
 |-  ( ph -> ( Im ` A ) = 0 )