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Metamath Proof Explorer

Theorem nndivred

Description: A positive integer is one or greater. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses nndivred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ )
nndivred.2 ⊢ ( 𝜑 → 𝐵 ∈ ℕ )
Assertion nndivred ( 𝜑 → ( 𝐴 / 𝐵 ) ∈ ℝ )

Proof

Step Hyp Ref Expression
1 nndivred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2 nndivred.2 ⊢ ( 𝜑 → 𝐵 ∈ ℕ )
3 nndivre ⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℕ ) → ( 𝐴 / 𝐵 ) ∈ ℝ )
4 1 2 3 syl2anc ⊢ ( 𝜑 → ( 𝐴 / 𝐵 ) ∈ ℝ )