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 ∈ ℂ → ( ( 𝐴 ↑ 2 ) ≠ 0 ↔ 𝐴 ≠ 0 ) )

Proof

Step	Hyp	Ref	Expression
1		sqeq0	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 ↑ 2 ) = 0 ↔ 𝐴 = 0 ) )
2	1	necon3bid	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 ↑ 2 ) ≠ 0 ↔ 𝐴 ≠ 0 ) )