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 )