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Metamath Proof Explorer

Theorem sqeq0d

Description: A number is zero iff its square is zero. (Contributed by Mario Carneiro, 28-May-2016)

Step	Hyp	Ref	Expression
1		expcld.1	$⊢ φ \to A \in ℂ$
2		sqeq0d.1	$⊢ φ \to A^{2} = 0$
3		2nn	$⊢ 2 \in ℕ$
4	3	a1i	$⊢ φ \to 2 \in ℕ$
5	1 4 2	expeq0d	$⊢ φ \to A = 0$