Theorem sqmuld

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

	Ref	Expression
Hypotheses	expcld.1	$$⊢\phi \to A\in ℂ$$
	mulexpd.2	$$⊢\phi \to B\in ℂ$$
Assertion	sqmuld	$$⊢\phi \to {AB}^2=A^2{B}^2$$

Proof

Step	Hyp	Ref	Expression
1		expcld.1	$$⊢\phi \to A\in ℂ$$
2		mulexpd.2	$$⊢\phi \to B\in ℂ$$
3		sqmul	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to {AB}^2=A^2{B}^2$$
4	1 2 3	syl2anc	$$⊢\phi \to {AB}^2=A^2{B}^2$$