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Metamath Proof Explorer

Theorem expne0

Description: A positive integer power is nonzero if and only if its base is nonzero. (Contributed by NM, 6-May-2005)

		Ref	Expression
	Assertion	expne0	$⊢ (A \in ℂ \land N \in ℕ) \to (A^{N} \neq 0 \leftrightarrow A \neq 0)$

Step	Hyp	Ref	Expression
1		expeq0	$⊢ (A \in ℂ \land N \in ℕ) \to (A^{N} = 0 \leftrightarrow A = 0)$
2	1	necon3bid	$⊢ (A \in ℂ \land N \in ℕ) \to (A^{N} \neq 0 \leftrightarrow A \neq 0)$