Theorem neg11i

Description: Negative is one-to-one. (Contributed by NM, 1-Aug-1999)

	Ref	Expression
Hypotheses	negidi.1	|- A e. CC
	pncan3i.2	|- B e. CC
Assertion	neg11i	|- ( -u A = -u B <-> A = B )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	|- A e. CC
2		pncan3i.2	|- B e. CC
3		neg11	|- ( ( A e. CC /\ B e. CC ) -> ( -u A = -u B <-> A = B ) )
4	1 2 3	mp2an	|- ( -u A = -u B <-> A = B )