Theorem negcon1i

Description: Negative contraposition law. (Contributed by NM, 25-Aug-1999)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
Assertion	negcon1i	$$⊢-A=B\leftrightarrow -B=A$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		negcon1	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A=B\leftrightarrow -B=A\right)$$
4	1 2 3	mp2an	$$⊢-A=B\leftrightarrow -B=A$$