Description: The square of a nonnegative number is a one-to-one function. (Contributed by NM, 29-Jul-1999) (Revised by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | msq11 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | le2msq | |
|
2 | le2msq | |
|
3 | 2 | ancoms | |
4 | 1 3 | anbi12d | |
5 | simpll | |
|
6 | simprl | |
|
7 | 5 6 | letri3d | |
8 | 5 5 | remulcld | |
9 | 6 6 | remulcld | |
10 | 8 9 | letri3d | |
11 | 4 7 10 | 3bitr4rd | |