Theorem ssct

Description: Any subset of a countable set is countable. (Contributed by Thierry Arnoux, 31-Jan-2017) Avoid ax-pow , ax-un . (Revised by BTernaryTau, 7-Dec-2024)

	Ref	Expression
Assertion	ssct	$$⊢\left(A\subseteq B\wedge B\preccurlyeq \mathrm{\omega }\right)\to A\preccurlyeq \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		domssl	$$⊢\left(A\subseteq B\wedge B\preccurlyeq \mathrm{\omega }\right)\to A\preccurlyeq \mathrm{\omega }$$