Description: Lemma to show a nonnegative number is zero. (Contributed by NM, 8-Oct-1999) (Proof shortened by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | lesub0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0red | |
|
2 | letri3 | |
|
3 | 1 2 | sylan2 | |
4 | ancom | |
|
5 | simpr | |
|
6 | 0red | |
|
7 | simpl | |
|
8 | lesub2 | |
|
9 | 5 6 7 8 | syl3anc | |
10 | 7 | recnd | |
11 | 10 | subid1d | |
12 | 11 | breq1d | |
13 | 9 12 | bitrd | |
14 | 13 | ancoms | |
15 | 14 | anbi2d | |
16 | 4 15 | syl5bb | |
17 | 3 16 | bitr2d | |