Metamath Proof Explorer


Theorem decnncl2

Description: Closure for a decimal integer (zero units place). (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Hypothesis decnncl2.1 ⊢ A ∈ ℕ
Assertion decnncl2 Could not format assertion : No typesetting found for |- ; A 0 e. NN with typecode |-

Proof

Step Hyp Ref Expression
1 decnncl2.1 ⊢ A ∈ ℕ
2 dfdec10 Could not format ; A 0 = ( ( ; 1 0 x. A ) + 0 ) : No typesetting found for |- ; A 0 = ( ( ; 1 0 x. A ) + 0 ) with typecode |-
3 10nn ⊢ 10 ∈ ℕ
4 3 1 numnncl2 ⊢ 10 ⁢ A + 0 ∈ ℕ
5 2 4 eqeltri Could not format ; A 0 e. NN : No typesetting found for |- ; A 0 e. NN with typecode |-