Theorem fict

Description: A finite set is countable (weaker version of isfinite ). (Contributed by Thierry Arnoux, 27-Mar-2018)

	Ref	Expression
Assertion	fict	⊢ ( 𝐴 ∈ Fin → 𝐴 ≼ ω )

Proof

Step	Hyp	Ref	Expression
1		isfinite	⊢ ( 𝐴 ∈ Fin ↔ 𝐴 ≺ ω )
2		sdomdom	⊢ ( 𝐴 ≺ ω → 𝐴 ≼ ω )
3	1 2	sylbi	⊢ ( 𝐴 ∈ Fin → 𝐴 ≼ ω )