Theorem sqeq0d

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

	Ref	Expression
Hypotheses	expcld.1	|- ( ph -> A e. CC )
	sqeq0d.1	|- ( ph -> ( A ^ 2 ) = 0 )
Assertion	sqeq0d	|- ( ph -> A = 0 )

Proof

Step	Hyp	Ref	Expression
1		expcld.1	|- ( ph -> A e. CC )
2		sqeq0d.1	|- ( ph -> ( A ^ 2 ) = 0 )
3		2nn	|- 2 e. NN
4	3	a1i	|- ( ph -> 2 e. NN )
5	1 4 2	expeq0d	|- ( ph -> A = 0 )