Theorem imcld

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

	Ref	Expression
Hypothesis	recld.1	|- ( ph -> A e. CC )
Assertion	imcld	|- ( ph -> ( Im ` A ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		recld.1	|- ( ph -> A e. CC )
2		imcl	|- ( A e. CC -> ( Im ` A ) e. RR )
3	1 2	syl	|- ( ph -> ( Im ` A ) e. RR )