deffunc H₁( Element of X) -> Element of Class E = EqClass (E,$1);
consider f being Function of X,(Class E) such that
A1: for x being Element of X holds f . x = H₁(x) from FUNCT_2:sch 4();
take f ; :: thesis: for x being Element of X holds f . x = EqClass (E,x)
thus for x being Element of X holds f . x = EqClass (E,x) by A1; :: thesis: verum