Metamath Proof Explorer

Theorem rprege0

Description: A positive real is a nonnegative real number. (Contributed by Mario Carneiro, 31-Jan-2014)

Ref Expression
Assertion rprege0 
|- ( A e. RR+ -> ( A e. RR /\ 0 <_ A ) )

Proof

Step Hyp Ref Expression
1 rpre 
 |-  ( A e. RR+ -> A e. RR )
2 rpge0 
 |-  ( A e. RR+ -> 0 <_ A )
3 1 2 jca 
 |-  ( A e. RR+ -> ( A e. RR /\ 0 <_ A ) )