Theorem subsqi

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

	Ref	Expression
Hypotheses	binom2.1	|- A e. CC
	binom2.2	|- B e. CC
Assertion	subsqi	|- ( ( A ^ 2 ) - ( B ^ 2 ) ) = ( ( A + B ) x. ( A - B ) )

Proof

Step	Hyp	Ref	Expression
1		binom2.1	|- A e. CC
2		binom2.2	|- B e. CC
3		subsq	|- ( ( A e. CC /\ B e. CC ) -> ( ( A ^ 2 ) - ( B ^ 2 ) ) = ( ( A + B ) x. ( A - B ) ) )
4	1 2 3	mp2an	|- ( ( A ^ 2 ) - ( B ^ 2 ) ) = ( ( A + B ) x. ( A - B ) )