Theorem sqrtmulii

Description: Square root distributes over multiplication. (Contributed by NM, 30-Jul-1999)

	Ref	Expression
Hypotheses	sqrtthi.1	|- A e. RR
	sqr11.1	|- B e. RR
	sqrmuli.1	|- 0 <_ A
	sqrmuli.2	|- 0 <_ B
Assertion	sqrtmulii	|- ( sqrt ` ( A x. B ) ) = ( ( sqrt ` A ) x. ( sqrt ` B ) )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	|- A e. RR
2		sqr11.1	|- B e. RR
3		sqrmuli.1	|- 0 <_ A
4		sqrmuli.2	|- 0 <_ B
5	1 2	sqrtmuli	|- ( ( 0 <_ A /\ 0 <_ B ) -> ( sqrt ` ( A x. B ) ) = ( ( sqrt ` A ) x. ( sqrt ` B ) ) )
6	3 4 5	mp2an	|- ( sqrt ` ( A x. B ) ) = ( ( sqrt ` A ) x. ( sqrt ` B ) )