Metamath Proof Explorer


Theorem sqrt1

Description: The square root of 1 is 1. (Contributed by NM, 31-Jul-1999)

Ref Expression
Assertion sqrt1
|- ( sqrt ` 1 ) = 1

Proof

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