reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;
reserve x for set;
reserve x for object;
reserve A1,A2,B1,B2 for non empty set,
  f for Function of A1,B1,
  g for Function of A2,B2,
  Y1 for non empty Subset of A1,
  Y2 for non empty Subset of A2;
reserve a,b,c,x,y,z,w,d for object;

theorem
 for a,c,b,d,x,y,z,w being object holds
  a,c,x,w are_mutually_distinct
  implies (a,c,x,w) --> (b,d,y,z) = { [a,b], [c,d],[x,y],[w,z] }
proof
 let a,c,b,d,x,y,z,w be object;
  assume
A1: a,c,x,w are_mutually_distinct;
  then
A2: a <> c;
A3: a <> x by A1;
A4: a <> w by A1;
A5: c <> x by A1;
A6: c <> w by A1;
A7: x<>w by A1;
  set m=(a,c) --> (b,d), n = (x,w) --> (y,z);
A8: dom m = {a,c} by Th62;
A9: dom n = {x,w} by Th62;
A10: not a in {x,w} by A3,A4,TARSKI:def 2;
  not c in {x,w} by A5,A6,TARSKI:def 2;
  then (a,c,x,w) --> (b,d,y,z) = m \/ n by A8,A9,A10,Th31,ZFMISC_1:51
    .={ [a,b], [c,d] } \/ n by A2,Th67
    .={ [a,b], [c,d] } \/ {[x,y],[w,z]} by A7,Th67
    .={ [a,b], [c,d], [x,y],[w,z]} by ENUMSET1:5;
  hence thesis;
end;
