Theorem neg11i

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

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
Assertion	neg11i	$$⊢-A=-B\leftrightarrow A=B$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		neg11	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A=-B\leftrightarrow A=B\right)$$
4	1 2 3	mp2an	$$⊢-A=-B\leftrightarrow A=B$$