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