Metamath Proof Explorer


Theorem 2pos

Description: The number 2 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 2pos
|- 0 < 2

Proof

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