Description: Square root of square. (Contributed by Mario Carneiro, 29-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | resqrcld.1 | |- ( ph -> A e. RR ) |
|
resqrcld.2 | |- ( ph -> 0 <_ A ) |
||
Assertion | sqrtmsqd | |- ( ph -> ( sqrt ` ( A x. A ) ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resqrcld.1 | |- ( ph -> A e. RR ) |
|
2 | resqrcld.2 | |- ( ph -> 0 <_ A ) |
|
3 | sqrtmsq | |- ( ( A e. RR /\ 0 <_ A ) -> ( sqrt ` ( A x. A ) ) = A ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( sqrt ` ( A x. A ) ) = A ) |