Theorem unfid

Description: The union of two finite sets is finite. (Contributed by Glauco Siliprandi, 5-Feb-2022)

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

Proof

Step	Hyp	Ref	Expression
1		unfid.1	|- ( ph -> A e. Fin )
2		unfid.2	|- ( ph -> B e. Fin )
3		unfi	|- ( ( A e. Fin /\ B e. Fin ) -> ( A u. B ) e. Fin )
4	1 2 3	syl2anc	|- ( ph -> ( A u. B ) e. Fin )