Theorem nnsdom

Description: A natural number is strictly dominated by the set of natural numbers. Example 3 of Enderton p. 146. (Contributed by NM, 28-Oct-2003)

	Ref	Expression
Assertion	nnsdom	$$⊢A\in \mathrm{\omega }\to A\prec \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		omex	$$⊢\mathrm{\omega }\in \mathrm{V}$$
2		nnsdomg	$$⊢\left(\mathrm{\omega }\in \mathrm{V}\wedge A\in \mathrm{\omega }\right)\to A\prec \mathrm{\omega }$$
3	1 2	mpan	$$⊢A\in \mathrm{\omega }\to A\prec \mathrm{\omega }$$