Theorem sqeq0i

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

	Ref	Expression
Hypothesis	sqval.1	⊢ 𝐴 ∈ ℂ
Assertion	sqeq0i	⊢ ( ( 𝐴 ↑ 2 ) = 0 ↔ 𝐴 = 0 )

Proof

Step	Hyp	Ref	Expression
1		sqval.1	⊢ 𝐴 ∈ ℂ
2		sqeq0	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 ↑ 2 ) = 0 ↔ 𝐴 = 0 ) )
3	1 2	ax-mp	⊢ ( ( 𝐴 ↑ 2 ) = 0 ↔ 𝐴 = 0 )