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Metamath Proof Explorer

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	$⊢ ℑ (A) \in ℝ$

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