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Metamath Proof Explorer

Theorem gt0ne0ii

Description: Positive implies nonzero. (Contributed by NM, 15-May-1999)

Ref Expression
Hypotheses lt2.1 ⊢ A ∈ ℝ
gt0ne0i.2 ⊢ 0 < A
Assertion gt0ne0ii ⊢ A ≠ 0

Proof

Step Hyp Ref Expression
1 lt2.1 ⊢ A ∈ ℝ
2 gt0ne0i.2 ⊢ 0 < A
3 1 gt0ne0i ⊢ 0 < A → A ≠ 0
4 2 3 ax-mp ⊢ A ≠ 0