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
Assertion eqnegd φA=AA=0

Proof

Step Hyp Ref Expression
1 eqnegd.1 φA
2 eqneg AA=AA=0
3 1 2 syl φA=AA=0