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 ) |
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 ) |