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Metamath Proof Explorer

Theorem ge0p1rpd

Description: A nonnegative number plus one is a positive number. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypotheses rpgecld.1 ⊢ φ → A ∈ ℝ
ge0p1rp.2 ⊢ φ → 0 ≤ A
Assertion ge0p1rpd ⊢ φ → A + 1 ∈ ℝ +

Proof

Step Hyp Ref Expression
1 rpgecld.1 ⊢ φ → A ∈ ℝ
2 ge0p1rp.2 ⊢ φ → 0 ≤ A
3 ge0p1rp ⊢ A ∈ ℝ ∧ 0 ≤ A → A + 1 ∈ ℝ +
4 1 2 3 syl2anc ⊢ φ → A + 1 ∈ ℝ +