Description: The square root of 4 is 2. (Contributed by NM, 3-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Assertion | sqrt4 | |- ( sqrt ` 4 ) = 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sq2 | |- ( 2 ^ 2 ) = 4 |
|
2 | 1 | fveq2i | |- ( sqrt ` ( 2 ^ 2 ) ) = ( sqrt ` 4 ) |
3 | 2re | |- 2 e. RR |
|
4 | 0le2 | |- 0 <_ 2 |
|
5 | sqrtsq | |- ( ( 2 e. RR /\ 0 <_ 2 ) -> ( sqrt ` ( 2 ^ 2 ) ) = 2 ) |
|
6 | 3 4 5 | mp2an | |- ( sqrt ` ( 2 ^ 2 ) ) = 2 |
7 | 2 6 | eqtr3i | |- ( sqrt ` 4 ) = 2 |