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Metamath Proof Explorer

Theorem negcon2i

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

Ref Expression
Hypotheses negidi.1 ⊢ A ∈ ℂ
pncan3i.2 ⊢ B ∈ ℂ
Assertion negcon2i ⊢ A = − B ↔ B = − A

Proof

Step Hyp Ref Expression
1 negidi.1 ⊢ A ∈ ℂ
2 pncan3i.2 ⊢ B ∈ ℂ
3 negcon2 ⊢ A ∈ ℂ ∧ B ∈ ℂ → A = − B ↔ B = − A
4 1 2 3 mp2an ⊢ A = − B ↔ B = − A