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Metamath Proof Explorer

Theorem numcl

Description: Closure for a decimal integer (with units place). (Contributed by Mario Carneiro, 18-Feb-2014)

Ref Expression
Hypotheses numnncl.1 ⊢ T ∈ ℕ 0
numnncl.2 ⊢ A ∈ ℕ 0
numcl.2 ⊢ B ∈ ℕ 0
Assertion numcl ⊢ T ⁢ A + B ∈ ℕ 0

Proof

Step Hyp Ref Expression
1 numnncl.1 ⊢ T ∈ ℕ 0
2 numnncl.2 ⊢ A ∈ ℕ 0
3 numcl.2 ⊢ B ∈ ℕ 0
4 1 2 nn0mulcli ⊢ T ⁢ A ∈ ℕ 0
5 4 3 nn0addcli ⊢ T ⁢ A + B ∈ ℕ 0