Theorem subsqi

Description: Factor the difference of two squares. (Contributed by NM, 7-Feb-2005)

	Ref	Expression
Hypotheses	binom2.1	$$⊢A\in ℂ$$
	binom2.2	$$⊢B\in ℂ$$
Assertion	subsqi	$$⊢A^2-B^2=\left(A+B\right)\left(A-B\right)$$

Proof

Step	Hyp	Ref	Expression
1		binom2.1	$$⊢A\in ℂ$$
2		binom2.2	$$⊢B\in ℂ$$
3		subsq	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A^2-B^2=\left(A+B\right)\left(A-B\right)$$
4	1 2 3	mp2an	$$⊢A^2-B^2=\left(A+B\right)\left(A-B\right)$$