Theorem imcli

Description: The imaginary part of a complex number is real (closure law). (Contributed by NM, 11-May-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	imcli	⊢ ( ℑ ‘ 𝐴 ) ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		imcl	⊢ ( 𝐴 ∈ ℂ → ( ℑ ‘ 𝐴 ) ∈ ℝ )
3	1 2	ax-mp	⊢ ( ℑ ‘ 𝐴 ) ∈ ℝ