Metamath Proof Explorer


Theorem 9pos

Description: The number 9 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 9pos
|- 0 < 9

Proof

Step Hyp Ref Expression
1 8re
 |-  8 e. RR
2 1re
 |-  1 e. RR
3 8pos
 |-  0 < 8
4 0lt1
 |-  0 < 1
5 1 2 3 4 addgt0ii
 |-  0 < ( 8 + 1 )
6 df-9
 |-  9 = ( 8 + 1 )
7 5 6 breqtrri
 |-  0 < 9