Metamath Proof Explorer

Theorem rphalflt

Description: Half of a positive real is less than the original number. (Contributed by Mario Carneiro, 21-May-2014)

Ref Expression
Assertion rphalflt 
|- ( A e. RR+ -> ( A / 2 ) < A )

Proof

Step Hyp Ref Expression
1 elrp 
 |-  ( A e. RR+ <-> ( A e. RR /\ 0 < A ) )
2 halfpos 
 |-  ( A e. RR -> ( 0 < A <-> ( A / 2 ) < A ) )
3 2 biimpa 
 |-  ( ( A e. RR /\ 0 < A ) -> ( A / 2 ) < A )
4 1 3 sylbi 
 |-  ( A e. RR+ -> ( A / 2 ) < A )