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Metamath Proof Explorer

Theorem deccl

Description: Closure for a numeral. (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Hypotheses	deccl.1	$⊢ A \in ℕ_{0}$
	deccl.2	$⊢ B \in ℕ_{0}$
Assertion	deccl	Could not format assertion : No typesetting found for \|- ; A B e. NN0 with typecode \|-

Step	Hyp	Ref	Expression
1		deccl.1	$⊢ A \in ℕ_{0}$
2		deccl.2	$⊢ B \in ℕ_{0}$
3		df-dec	Could not format ; A B = ( ( ( 9 + 1 ) x. A ) + B ) : No typesetting found for \|- ; A B = ( ( ( 9 + 1 ) x. A ) + B ) with typecode \|-
4		9nn0	$⊢ 9 \in ℕ_{0}$
5		1nn0	$⊢ 1 \in ℕ_{0}$
6	4 5	nn0addcli	$⊢ 9 + 1 \in ℕ_{0}$
7	6 1 2	numcl	$⊢ (9 + 1) A + B \in ℕ_{0}$
8	3 7	eqeltri	Could not format ; A B e. NN0 : No typesetting found for \|- ; A B e. NN0 with typecode \|-