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	$$⊢\phi \to A\in ℂ$$
Assertion	sqrtcld	$$⊢\phi \to \sqrt{A}\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		abscld.1	$$⊢\phi \to A\in ℂ$$
2		sqrtcl	$$⊢A\in ℂ\to \sqrt{A}\in ℂ$$
3	1 2	syl	$$⊢\phi \to \sqrt{A}\in ℂ$$