Description: The square root of 1 is 1. (Contributed by NM, 31-Jul-1999)
Ref | Expression | ||
---|---|---|---|
Assertion | sqrt1 | |- ( sqrt ` 1 ) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sq1 | |- ( 1 ^ 2 ) = 1 |
|
2 | 1 | fveq2i | |- ( sqrt ` ( 1 ^ 2 ) ) = ( sqrt ` 1 ) |
3 | 1re | |- 1 e. RR |
|
4 | 0le1 | |- 0 <_ 1 |
|
5 | sqrtsq | |- ( ( 1 e. RR /\ 0 <_ 1 ) -> ( sqrt ` ( 1 ^ 2 ) ) = 1 ) |
|
6 | 3 4 5 | mp2an | |- ( sqrt ` ( 1 ^ 2 ) ) = 1 |
7 | 2 6 | eqtr3i | |- ( sqrt ` 1 ) = 1 |