Metamath Proof Explorer

Theorem ltaddposi

Description: Adding a positive number to another number increases it. (Contributed by NM, 25-Aug-1999)

Ref Expression
Hypotheses lt2.1 
|- A e. RR
lt2.2 
|- B e. RR
Assertion ltaddposi 
|- ( 0 < A <-> B < ( B + A ) )

Proof

Step Hyp Ref Expression
1 lt2.1 
 |-  A e. RR
2 lt2.2 
 |-  B e. RR
3 ltaddpos 
 |-  ( ( A e. RR /\ B e. RR ) -> ( 0 < A <-> B < ( B + A ) ) )
4 1 2 3 mp2an 
 |-  ( 0 < A <-> B < ( B + A ) )