Theorem sqrt4

Description: The square root of 4 is 2. (Contributed by NM, 3-Aug-1999)

	Ref	Expression
Assertion	sqrt4	|- ( sqrt ` 4 ) = 2

Proof

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