Theorem ssfid

Description: A subset of a finite set is finite, deduction version of ssfi . (Contributed by Glauco Siliprandi, 21-Nov-2020)

	Ref	Expression
Hypotheses	ssfid.1	|- ( ph -> A e. Fin )
	ssfid.2	|- ( ph -> B C_ A )
Assertion	ssfid	|- ( ph -> B e. Fin )

Proof

Step	Hyp	Ref	Expression
1		ssfid.1	|- ( ph -> A e. Fin )
2		ssfid.2	|- ( ph -> B C_ A )
3		ssfi	|- ( ( A e. Fin /\ B C_ A ) -> B e. Fin )
4	1 2 3	syl2anc	|- ( ph -> B e. Fin )