This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem decnncl

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

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

Step	Hyp	Ref	Expression
1		decnncl.1	$⊢ A \in ℕ_{0}$
2		decnncl.2	$⊢ B \in ℕ$
3		dfdec10	Could not format ; A B = ( ( ; 1 0 x. A ) + B ) : No typesetting found for \|- ; A B = ( ( ; 1 0 x. A ) + B ) with typecode \|-
4		10nn0	$⊢ 10 \in ℕ_{0}$
5	4 1 2	numnncl	$⊢ 10 A + B \in ℕ$
6	3 5	eqeltri	Could not format ; A B e. NN : No typesetting found for \|- ; A B e. NN with typecode \|-