Theorem sqmuld

Description: Distribution of squaring over multiplication. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	expcld.1	|- ( ph -> A e. CC )
	mulexpd.2	|- ( ph -> B e. CC )
Assertion	sqmuld	|- ( ph -> ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		expcld.1	|- ( ph -> A e. CC )
2		mulexpd.2	|- ( ph -> B e. CC )
3		sqmul	|- ( ( A e. CC /\ B e. CC ) -> ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( ( A x. B ) ^ 2 ) = ( ( A ^ 2 ) x. ( B ^ 2 ) ) )