Metamath Proof Explorer


Theorem 5pos

Description: The number 5 is positive. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 5pos 0 < 5

Proof

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