Metamath Proof Explorer

Theorem 7pos

Description: The number 7 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 7pos 
|- 0 < 7

Proof

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