Metamath Proof Explorer

Theorem negeq0d

Description: A number is zero iff its negative is zero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis negidd.1 
|- ( ph -> A e. CC )
Assertion negeq0d 
|- ( ph -> ( A = 0 <-> -u A = 0 ) )

Proof

Step Hyp Ref Expression
1 negidd.1 
 |-  ( ph -> A e. CC )
2 negeq0 
 |-  ( A e. CC -> ( A = 0 <-> -u A = 0 ) )
3 1 2 syl 
 |-  ( ph -> ( A = 0 <-> -u A = 0 ) )