Theorem sqcl

Description: Closure of square. (Contributed by NM, 10-Aug-1999)

	Ref	Expression
Assertion	sqcl	$$⊢A\in ℂ\to A^2\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		sqval	$$⊢A\in ℂ\to A^2=AA$$
2		mulcl	$$⊢\left(A\in ℂ\wedge A\in ℂ\right)\to AA\in ℂ$$
3	2	anidms	$$⊢A\in ℂ\to AA\in ℂ$$
4	1 3	eqeltrd	$$⊢A\in ℂ\to A^2\in ℂ$$