Theorem sqeq0i

Description: A complex number is zero iff its square is zero. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	sqval.1	$$⊢A\in ℂ$$
Assertion	sqeq0i	$$⊢A^2=0\leftrightarrow A=0$$

Proof

Step	Hyp	Ref	Expression
1		sqval.1	$$⊢A\in ℂ$$
2		sqeq0	$$⊢A\in ℂ\to \left(A^2=0\leftrightarrow A=0\right)$$
3	1 2	ax-mp	$$⊢A^2=0\leftrightarrow A=0$$