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	$$⊢A\in ℂ$$
Assertion	imcli	$$⊢\Im \left(A\right)\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		imcl	$$⊢A\in ℂ\to \Im \left(A\right)\in ℝ$$
3	1 2	ax-mp	$$⊢\Im \left(A\right)\in ℝ$$