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Metamath Proof Explorer

Theorem gzcn

Description: A gaussian integer is a complex number. (Contributed by Mario Carneiro, 14-Jul-2014)

		Ref	Expression
	Assertion	gzcn	$⊢ A \in ℤ [i] \to A \in ℂ$

Step	Hyp	Ref	Expression
1		elgz	$⊢ A \in ℤ [i] \leftrightarrow (A \in ℂ \land ℜ (A) \in ℤ \land ℑ (A) \in ℤ)$
2	1	simp1bi	$⊢ A \in ℤ [i] \to A \in ℂ$