Description: Closure for a decimal integer (with units place). (Contributed by Mario Carneiro, 18-Feb-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | numnncl.1 | ⊢ 𝑇 ∈ ℕ0 | |
numnncl.2 | ⊢ 𝐴 ∈ ℕ0 | ||
numcl.2 | ⊢ 𝐵 ∈ ℕ0 | ||
Assertion | numcl | ⊢ ( ( 𝑇 · 𝐴 ) + 𝐵 ) ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | numnncl.1 | ⊢ 𝑇 ∈ ℕ0 | |
2 | numnncl.2 | ⊢ 𝐴 ∈ ℕ0 | |
3 | numcl.2 | ⊢ 𝐵 ∈ ℕ0 | |
4 | 1 2 | nn0mulcli | ⊢ ( 𝑇 · 𝐴 ) ∈ ℕ0 |
5 | 4 3 | nn0addcli | ⊢ ( ( 𝑇 · 𝐴 ) + 𝐵 ) ∈ ℕ0 |