Description: A square of a real is nonnegative. (Contributed by NM, 18-Oct-1999)
Ref | Expression | ||
---|---|---|---|
Assertion | sqge0 | |- ( A e. RR -> 0 <_ ( A ^ 2 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | msqge0 | |- ( A e. RR -> 0 <_ ( A x. A ) ) |
|
2 | recn | |- ( A e. RR -> A e. CC ) |
|
3 | sqval | |- ( A e. CC -> ( A ^ 2 ) = ( A x. A ) ) |
|
4 | 2 3 | syl | |- ( A e. RR -> ( A ^ 2 ) = ( A x. A ) ) |
5 | 1 4 | breqtrrd | |- ( A e. RR -> 0 <_ ( A ^ 2 ) ) |