defpred S₁[ set ] means ( $1 in X & $1 is Ordinal );
let Y, Z be set ; :: thesis: ( ( for x being set holds
( x in Y iff ( x in X & x is Ordinal ) ) ) & ( for x being set holds
( x in Z iff ( x in X & x is Ordinal ) ) ) implies Y = Z )
assume that
A1: for x being set holds
( x in Y iff S₁[x] ) and
A2: for x being set holds
( x in Z iff S₁[x] ) ; :: thesis: Y = Z
thus Y = Z from XBOOLE_0:sch 2(A1, A2); :: thesis: verum