Metamath Proof Explorer

Theorem 8pos

Description: The number 8 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 8pos 
|- 0 < 8

Proof

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