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Metamath Proof Explorer

Theorem nn0addcli

Description: Closure of addition of nonnegative integers, inference form. (Contributed by Raph Levien, 10-Dec-2002)

Ref Expression
Hypotheses nn0addcli.1 ⊢ 𝑀 ∈ ℕ0
nn0addcli.2 ⊢ 𝑁 ∈ ℕ0
Assertion nn0addcli ( 𝑀 + 𝑁 ) ∈ ℕ0

Proof

Step Hyp Ref Expression
1 nn0addcli.1 ⊢ 𝑀 ∈ ℕ0
2 nn0addcli.2 ⊢ 𝑁 ∈ ℕ0
3 nn0addcl ⊢ ( ( 𝑀 ∈ ℕ0 ∧ 𝑁 ∈ ℕ0 ) → ( 𝑀 + 𝑁 ) ∈ ℕ0 )
4 1 2 3 mp2an ⊢ ( 𝑀 + 𝑁 ) ∈ ℕ0