defpred S₁[ set ] means $1 is Chain of f;
consider X being set such that
A1: for x being set holds
( x in X iff ( x in bool the carrier of A & S₁[x] ) ) from XFAMILY:sch 1();
take X ; :: thesis: for x being set holds
( x in X iff x is Chain of f )
let x be set ; :: thesis: ( x in X iff x is Chain of f )
thus ( x in X implies x is Chain of f ) by A1; :: thesis: ( x is Chain of f implies x in X )
assume x is Chain of f ; :: thesis: x in X
hence x in X by A1; :: thesis: verum