reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;

theorem Th22:
  x<>y & not y in union X & not y in union Y  implies
    Ext(X,x,y) misses swap(Y,x,y)
proof
  assume
A1: x<>y & not y in union X & not y in union Y;
  assume Ext(X,x,y) meets swap(Y,x,y);
  then consider a be object such that
A2: a in Ext(X,x,y) & a in swap(Y,x,y) by XBOOLE_0:3;
  reconsider a as set by TARSKI:1;
  x in a iff not y in a by A2,A1,Th14;
  hence thesis by A2,A1,Th17;
end;
