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Metamath Proof Explorer

Theorem eqnegd

Description: A complex number equals its negative iff it is zero. Deduction form of eqneg . (Contributed by David Moews, 28-Feb-2017)

Ref Expression
Hypothesis eqnegd.1 ⊢ φ → A ∈ ℂ
Assertion eqnegd ⊢ φ → A = − A ↔ A = 0

Proof

Step Hyp Ref Expression
1 eqnegd.1 ⊢ φ → A ∈ ℂ
2 eqneg ⊢ A ∈ ℂ → A = − A ↔ A = 0
3 1 2 syl ⊢ φ → A = − A ↔ A = 0