Description: The absolute value of a number is zero iff the number is zero. Proposition 10-3.7(c) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | abscld.1 | |
|
absne0d.2 | |
||
Assertion | absne0d | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abscld.1 | |
|
2 | absne0d.2 | |
|
3 | 1 | abs00ad | |
4 | 3 | necon3bid | |
5 | 2 4 | mpbird | |