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 = - 𝐴𝐴 = 0 )

Proof

Step Hyp Ref Expression
1 divclz.1 𝐴 ∈ ℂ
2 eqneg ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴𝐴 = 0 ) )
3 1 2 ax-mp ( 𝐴 = - 𝐴𝐴 = 0 )