defpred S₁[ object ] means ex x being bound_QC-variable of Al ex p being Element of CQC-WFF Al st $1 = Ex (x,p);
let A1, A2 be Subset of (CQC-WFF Al); :: thesis: ( ( for a being set holds
( a in A1 iff ex x being bound_QC-variable of Al ex p being Element of CQC-WFF Al st a = Ex (x,p) ) ) & ( for a being set holds
( a in A2 iff ex x being bound_QC-variable of Al ex p being Element of CQC-WFF Al st a = Ex (x,p) ) ) implies A1 = A2 )
assume that
A2: for a being set holds
( a in A1 iff S₁[a] ) and
A3: for a being set holds
( a in A2 iff S₁[a] ) ; :: thesis: A1 = A2

now :: thesis: for a being object holds
( a in A1 iff a in A2 )

let a be object ; :: thesis: ( a in A1 iff a in A2 )
( a in A1 iff S₁[a] ) by A2;
hence ( a in A1 iff a in A2 ) by A3; :: thesis: verum

end;

hence A1 = A2 by TARSKI:2; :: thesis: verum