let R be non empty right_complementable distributive left_unital Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for I being Ideal of R
for a being Element of R holds Class ((EqRel (R,I)),a) is Element of (R / I)
let I be Ideal of R; :: thesis: for a being Element of R holds Class ((EqRel (R,I)),a) is Element of (R / I)
let a be Element of R; :: thesis: Class ((EqRel (R,I)),a) is Element of (R / I)
the carrier of (R / I) = Class (EqRel (R,I)) by Def6;
hence Class ((EqRel (R,I)),a) is Element of (R / I) by EQREL_1:def 3; :: thesis: verum