Theorem sqrtcld

Description: Closure of the square root function over the complex numbers. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	abscld.1	|- ( ph -> A e. CC )
Assertion	sqrtcld	|- ( ph -> ( sqrt ` A ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		abscld.1	|- ( ph -> A e. CC )
2		sqrtcl	|- ( A e. CC -> ( sqrt ` A ) e. CC )
3	1 2	syl	|- ( ph -> ( sqrt ` A ) e. CC )