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Metamath Proof Explorer

Theorem sqne0

Description: A complex number is nonzero if and only if its square is nonzero. (Contributed by NM, 11-Mar-2006)

		Ref	Expression
	Assertion	sqne0	$⊢ A \in ℂ \to (A^{2} \neq 0 \leftrightarrow A \neq 0)$

Step	Hyp	Ref	Expression
1		sqeq0	$⊢ A \in ℂ \to (A^{2} = 0 \leftrightarrow A = 0)$
2	1	necon3bid	$⊢ A \in ℂ \to (A^{2} \neq 0 \leftrightarrow A \neq 0)$