Theorem nn0xnn0d

Description: A standard nonnegative integer is an extended nonnegative integer, deduction form. (Contributed by AV, 10-Dec-2020)

	Ref	Expression
Hypothesis	nn0xnn0d.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
Assertion	nn0xnn0d	$$⊢\phi \to A\in {\mathbb{N}}_0^{*}$$

Proof

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
2		nn0ssxnn0	$$⊢{\mathbb{N}}_0\subseteq {\mathbb{N}}_0^{*}$$
3	2 1	sselid	$$⊢\phi \to A\in {\mathbb{N}}_0^{*}$$