reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem Th76:
  A c= B implies union A c= union B
proof
  assume
A1: A c= B;
  let x;
  assume x in union A;
  then consider Y such that
A2: x in Y and
A3: Y in A by TARSKI:def 4;
  Y in B by A1,A3;
  hence thesis by A2,TARSKI:def 4;
end;
