Theorem sqmuli

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

	Ref	Expression
Hypotheses	sqval.1	$$⊢A\in ℂ$$
	sqmul.2	$$⊢B\in ℂ$$
Assertion	sqmuli	$$⊢{AB}^2=A^2{B}^2$$

Proof

Step	Hyp	Ref	Expression
1		sqval.1	$$⊢A\in ℂ$$
2		sqmul.2	$$⊢B\in ℂ$$
3		sqmul	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to {AB}^2=A^2{B}^2$$
4	1 2 3	mp2an	$$⊢{AB}^2=A^2{B}^2$$