Theorem negcon1d

Description: Contraposition law for unary minus. Deduction form of negcon1 . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	negidd.1	$$⊢\phi \to A\in ℂ$$
	negcon1d.2	$$⊢\phi \to B\in ℂ$$
Assertion	negcon1d	$$⊢\phi \to \left(-A=B\leftrightarrow -B=A\right)$$

Proof

Step	Hyp	Ref	Expression
1		negidd.1	$$⊢\phi \to A\in ℂ$$
2		negcon1d.2	$$⊢\phi \to B\in ℂ$$
3		negcon1	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(-A=B\leftrightarrow -B=A\right)$$
4	1 2 3	syl2anc	$$⊢\phi \to \left(-A=B\leftrightarrow -B=A\right)$$