reserve R for commutative Ring;
reserve A for non degenerated commutative Ring;
reserve I,J,q for Ideal of A;
reserve p for prime Ideal of A;
reserve M,M1,M2 for Ideal of A/q;

theorem
    I c= J implies (canHom q).:I c= (canHom q).:J
    proof
      assume
A1:   I c= J;
      for x be Element of the carrier of A/q st x in (canHom q).:I
      holds x in (canHom q).:J
      proof
        let x be Element of the carrier of A/q;
        assume x in (canHom q).:I; then
        consider x0 being object such that
A3:     x0 in dom canHom(q) and
A4:     x0 in I and
A5:     x = (canHom(q)).x0 by FUNCT_1:def 6;
        thus thesis by A5,A1,A4,A3,FUNCT_1:def 6;
      end;
      hence thesis;
    end;
