Theorem fict

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

	Ref	Expression
Assertion	fict	$$⊢A\in \mathrm{Fin}\to A\preccurlyeq \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		isfinite	$$⊢A\in \mathrm{Fin}\leftrightarrow A\prec \mathrm{\omega }$$
2		sdomdom	$$⊢A\prec \mathrm{\omega }\to A\preccurlyeq \mathrm{\omega }$$
3	1 2	sylbi	$$⊢A\in \mathrm{Fin}\to A\preccurlyeq \mathrm{\omega }$$