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Metamath Proof Explorer

Theorem nn0mulcli

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

Ref Expression
Hypotheses nn0addcli.1 ⊢ M ∈ ℕ 0
nn0addcli.2 ⊢ N ∈ ℕ 0
Assertion nn0mulcli ⊢ M ⋅ N ∈ ℕ 0

Proof

Step Hyp Ref Expression
1 nn0addcli.1 ⊢ M ∈ ℕ 0
2 nn0addcli.2 ⊢ N ∈ ℕ 0
3 nn0mulcl ⊢ M ∈ ℕ 0 ∧ N ∈ ℕ 0 → M ⋅ N ∈ ℕ 0
4 1 2 3 mp2an ⊢ M ⋅ N ∈ ℕ 0