Theorem sqcl

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

	Ref	Expression
Assertion	sqcl	|- ( A e. CC -> ( A ^ 2 ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		sqval	|- ( A e. CC -> ( A ^ 2 ) = ( A x. A ) )
2		mulcl	|- ( ( A e. CC /\ A e. CC ) -> ( A x. A ) e. CC )
3	2	anidms	|- ( A e. CC -> ( A x. A ) e. CC )
4	1 3	eqeltrd	|- ( A e. CC -> ( A ^ 2 ) e. CC )