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Metamath Proof Explorer

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	$⊢ (A \in ℕ_{0} \land B \in ℕ_{0}) \to A + B \in ℝ$

Step	Hyp	Ref	Expression
1		nn0addcl	$⊢ (A \in ℕ_{0} \land B \in ℕ_{0}) \to A + B \in ℕ_{0}$
2	1	nn0red	$⊢ (A \in ℕ_{0} \land B \in ℕ_{0}) \to A + B \in ℝ$