Metamath Proof Explorer


Theorem negne0d

Description: The negative of a nonzero number is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses negidd.1
|- ( ph -> A e. CC )
negne0d.2
|- ( ph -> A =/= 0 )
Assertion negne0d
|- ( ph -> -u A =/= 0 )

Proof

Step Hyp Ref Expression
1 negidd.1
 |-  ( ph -> A e. CC )
2 negne0d.2
 |-  ( ph -> A =/= 0 )
3 1 negne0bd
 |-  ( ph -> ( A =/= 0 <-> -u A =/= 0 ) )
4 2 3 mpbid
 |-  ( ph -> -u A =/= 0 )