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 ( 𝜑𝐴 ∈ ℂ )
Assertion eqnegd ( 𝜑 → ( 𝐴 = - 𝐴𝐴 = 0 ) )

Proof

Step Hyp Ref Expression
1 eqnegd.1 ( 𝜑𝐴 ∈ ℂ )
2 eqneg ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴𝐴 = 0 ) )
3 1 2 syl ( 𝜑 → ( 𝐴 = - 𝐴𝐴 = 0 ) )