Theorem fiufl

Description: A finite set satisfies the ultrafilter lemma. (Contributed by Mario Carneiro, 26-Aug-2015)

	Ref	Expression
Assertion	fiufl	|- ( X e. Fin -> X e. UFL )

Proof

Step	Hyp	Ref	Expression
1		pwfi	|- ( X e. Fin <-> ~P X e. Fin )
2		pwfi	|- ( ~P X e. Fin <-> ~P ~P X e. Fin )
3		finnum	|- ( ~P ~P X e. Fin -> ~P ~P X e. dom card )
4		numufl	|- ( ~P ~P X e. dom card -> X e. UFL )
5	3 4	syl	|- ( ~P ~P X e. Fin -> X e. UFL )
6	2 5	sylbi	|- ( ~P X e. Fin -> X e. UFL )
7	1 6	sylbi	|- ( X e. Fin -> X e. UFL )