Metamath Proof Explorer


Theorem eqnegi

Description: A number equal to its negative is zero. (Contributed by NM, 29-May-1999)

Ref Expression
Hypothesis divclz.1 ⊢ A ∈ ℂ
Assertion eqnegi ⊢ A = − A ↔ A = 0

Proof

Step Hyp Ref Expression
1 divclz.1 ⊢ A ∈ ℂ
2 eqneg ⊢ A ∈ ℂ → A = − A ↔ A = 0
3 1 2 ax-mp ⊢ A = − A ↔ A = 0