defpred S₁[ set ] means $1 is Tolerance of ;
consider a being set such that
A1: for x being set holds
( x in a iff ( x in bool [:X,X:] & S₁[x] ) ) from XBOOLE_0:sch 1();
take a ; :: thesis: for x being set holds
( x in a iff x is Tolerance of )
let x be set ; :: thesis: ( x in a iff x is Tolerance of )
thus ( x in a implies x is Tolerance of ) by A1; :: thesis: ( x is Tolerance of implies x in a )
assume x is Tolerance of ; :: thesis: x in a
hence x in a by A1; :: thesis: verum