Metamath Proof Explorer

Theorem 3pos

Description: The number 3 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 3pos 
|- 0 < 3

Proof

Step Hyp Ref Expression
1 2re 
 |-  2 e. RR
2 1re 
 |-  1 e. RR
3 2pos 
 |-  0 < 2
4 0lt1 
 |-  0 < 1
5 1 2 3 4 addgt0ii 
 |-  0 < ( 2 + 1 )
6 df-3 
 |-  3 = ( 2 + 1 )
7 5 6 breqtrri 
 |-  0 < 3