Theorem sqsqrtd

Description: Square root theorem. Theorem I.35 of Apostol p. 29. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	abscld.1	$$⊢\phi \to A\in ℂ$$
Assertion	sqsqrtd	$$⊢\phi \to {\sqrt{A}}^2=A$$

Proof

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