Theorem subeq0i

Description: If the difference between two numbers is zero, they are equal. (Contributed by NM, 8-May-1999)

	Ref	Expression
Hypotheses	negidi.1	|- A e. CC
	pncan3i.2	|- B e. CC
Assertion	subeq0i	|- ( ( A - B ) = 0 <-> A = B )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	|- A e. CC
2		pncan3i.2	|- B e. CC
3		subeq0	|- ( ( A e. CC /\ B e. CC ) -> ( ( A - B ) = 0 <-> A = B ) )
4	1 2 3	mp2an	|- ( ( A - B ) = 0 <-> A = B )