Metamath Proof Explorer

Theorem negne0i

Description: The negative of a nonzero number is nonzero. (Contributed by NM, 30-Jul-2004)

Ref Expression
Hypotheses negidi.1 
|- A e. CC
negne0i.2 
|- A =/= 0
Assertion negne0i 
|- -u A =/= 0

Proof

Step Hyp Ref Expression
1 negidi.1 
 |-  A e. CC
2 negne0i.2 
 |-  A =/= 0
3 1 negne0bi 
 |-  ( A =/= 0 <-> -u A =/= 0 )
4 2 3 mpbi 
 |-  -u A =/= 0