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Metamath Proof Explorer

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	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ≼ ω ) → 𝐴 ≼ ω )

Proof

Step	Hyp	Ref	Expression
1		domssl	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ≼ ω ) → 𝐴 ≼ ω )