Theorem sqr00d

Description: A square root is zero iff its argument is 0. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	abscld.1	|- ( ph -> A e. CC )
	sqrt00d.2	|- ( ph -> ( sqrt ` A ) = 0 )
Assertion	sqr00d	|- ( ph -> A = 0 )

Proof

Step	Hyp	Ref	Expression
1		abscld.1	|- ( ph -> A e. CC )
2		sqrt00d.2	|- ( ph -> ( sqrt ` A ) = 0 )
3	1	sqsqrtd	|- ( ph -> ( ( sqrt ` A ) ^ 2 ) = A )
4	2	sq0id	|- ( ph -> ( ( sqrt ` A ) ^ 2 ) = 0 )
5	3 4	eqtr3d	|- ( ph -> A = 0 )