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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 ∈ ℝ
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