Metamath Proof Explorer


Theorem fclsfil

Description: Reverse closure for the cluster point predicate. (Contributed by Mario Carneiro, 11-Apr-2015) (Revised by Stefan O'Rear, 8-Aug-2015)

Ref Expression
Hypothesis fclsval.x X=J
Assertion fclsfil AJfClusFFFilX

Proof

Step Hyp Ref Expression
1 fclsval.x X=J
2 1 isfcls AJfClusFJTopFFilXsFAclsJs
3 2 simp2bi AJfClusFFFilX