Theorem sq0id

Description: If a number is zero, its square is zero. Deduction form of sq0i . Converse of sqeq0d . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypothesis	sq0id.1	⊢ ( 𝜑 → 𝐴 = 0 )
Assertion	sq0id	⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		sq0id.1	⊢ ( 𝜑 → 𝐴 = 0 )
2		sq0i	⊢ ( 𝐴 = 0 → ( 𝐴 ↑ 2 ) = 0 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) = 0 )