Theorem negcon1i

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

	Ref	Expression
Hypotheses	negidi.1	⊢ 𝐴 ∈ ℂ
	pncan3i.2	⊢ 𝐵 ∈ ℂ
Assertion	negcon1i	⊢ ( - 𝐴 = 𝐵 ↔ - 𝐵 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		pncan3i.2	⊢ 𝐵 ∈ ℂ
3		negcon1	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( - 𝐴 = 𝐵 ↔ - 𝐵 = 𝐴 ) )
4	1 2 3	mp2an	⊢ ( - 𝐴 = 𝐵 ↔ - 𝐵 = 𝐴 )