Metamath Proof Explorer

Theorem sqrtcli

Description: The square root of a nonnegative real is a real. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)

Ref Expression
Hypothesis sqrtthi.1 
|- A e. RR
Assertion sqrtcli 
|- ( 0 <_ A -> ( sqrt ` A ) e. RR )

Proof

Step Hyp Ref Expression
1 sqrtthi.1 
 |-  A e. RR
2 resqrtcl 
 |-  ( ( A e. RR /\ 0 <_ A ) -> ( sqrt ` A ) e. RR )
3 1 2 mpan 
 |-  ( 0 <_ A -> ( sqrt ` A ) e. RR )