Theorem nn0readdcl

Description: Closure law for addition of reals, restricted to nonnegative integers. (Contributed by Alexander van der Vekens, 6-Apr-2018)

	Ref	Expression
Assertion	nn0readdcl	⊢ ( ( 𝐴 ∈ ℕ0 ∧ 𝐵 ∈ ℕ0 ) → ( 𝐴 + 𝐵 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		nn0addcl	⊢ ( ( 𝐴 ∈ ℕ0 ∧ 𝐵 ∈ ℕ0 ) → ( 𝐴 + 𝐵 ) ∈ ℕ0 )
2	1	nn0red	⊢ ( ( 𝐴 ∈ ℕ0 ∧ 𝐵 ∈ ℕ0 ) → ( 𝐴 + 𝐵 ) ∈ ℝ )