Theorem sqne0

Description: A number is nonzero iff its square is nonzero. (Contributed by NM, 11-Mar-2006)

	Ref	Expression
Assertion	sqne0	$$⊢A\in ℂ\to \left(A^2\ne 0\leftrightarrow A\ne 0\right)$$

Proof

Step	Hyp	Ref	Expression
1		sqeq0	$$⊢A\in ℂ\to \left(A^2=0\leftrightarrow A=0\right)$$
2	1	necon3bid	$$⊢A\in ℂ\to \left(A^2\ne 0\leftrightarrow A\ne 0\right)$$