Theorem sqmuli

Description: Distribution of squaring over multiplication. (Contributed by NM, 3-Sep-1999)

	Ref	Expression
Hypotheses	sqval.1	|- A e. CC
	sqmul.2	|- B e. CC
Assertion	sqmuli	|- ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		sqval.1	|- A e. CC
2		sqmul.2	|- B e. CC
3		sqmul	|- ( ( A e. CC /\ B e. CC ) -> ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) ) )
4	1 2 3	mp2an	|- ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) )