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	$$⊢\phi \to A\in ℂ$$
Assertion	imcld	$$⊢\phi \to \Im \left(A\right)\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recld.1	$$⊢\phi \to A\in ℂ$$
2		imcl	$$⊢A\in ℂ\to \Im \left(A\right)\in ℝ$$
3	1 2	syl	$$⊢\phi \to \Im \left(A\right)\in ℝ$$