Theorem omensuc

Description: The set of natural numbers is equinumerous to its successor. (Contributed by NM, 30-Oct-2003)

	Ref	Expression
Assertion	omensuc	$$⊢\mathrm{\omega }\approx \mathrm{suc}\mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		omex	$$⊢\mathrm{\omega }\in \mathrm{V}$$
2		limom	$$⊢\mathrm{Lim}\mathrm{\omega }$$
3	2	limensuci	$$⊢\mathrm{\omega }\in \mathrm{V}\to \mathrm{\omega }\approx \mathrm{suc}\mathrm{\omega }$$
4	1 3	ax-mp	$$⊢\mathrm{\omega }\approx \mathrm{suc}\mathrm{\omega }$$