Metamath Proof Explorer

Theorem resqcl

Description: Closure of the square of a real number. (Contributed by NM, 18-Oct-1999)

Ref Expression
Assertion resqcl 
|- ( A e. RR -> ( A ^ 2 ) e. RR )

Proof

Step Hyp Ref Expression
1 2nn0 
 |-  2 e. NN0
2 reexpcl 
 |-  ( ( A e. RR /\ 2 e. NN0 ) -> ( A ^ 2 ) e. RR )
3 1 2 mpan2 
 |-  ( A e. RR -> ( A ^ 2 ) e. RR )