Description: The square of a real is nonnegative. (Contributed by NM, 3-Aug-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | resqcl.1 | |- A e. RR |
|
| Assertion | sqge0i | |- 0 <_ ( A ^ 2 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resqcl.1 | |- A e. RR |
|
| 2 | 1 | msqge0i | |- 0 <_ ( A x. A ) |
| 3 | 1 | recni | |- A e. CC |
| 4 | 3 | sqvali | |- ( A ^ 2 ) = ( A x. A ) |
| 5 | 2 4 | breqtrri | |- 0 <_ ( A ^ 2 ) |