Metamath Proof Explorer


Theorem rpne0d

Description: A positive real is nonzero. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis rpred.1 ⊢ φ → A ∈ ℝ +
Assertion rpne0d ⊢ φ → A ≠ 0

Proof

Step Hyp Ref Expression
1 rpred.1 ⊢ φ → A ∈ ℝ +
2 rpne0 ⊢ A ∈ ℝ + → A ≠ 0
3 1 2 syl ⊢ φ → A ≠ 0