 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve X,T for Subset of MC-wff;
 reserve F,G,H,p,q,r,t for Element of MC-wff;
 reserve s,h for MC-formula;
 reserve f for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve i,j for Element of NAT;
 reserve F1,F2,F3,F4,F5,F6,F7,F8,F9,F10,G for MC-formula;
 reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x for Element of MC-wff;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for object;

theorem Th63:
  {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} = {x2,x3,x4,x5,x6,x7,x8,x9,x10} \/ {x1}
proof
  now
    let x be object;
A1: x in {x1} iff x=x1 by TARSKI:def 1;
    x=x2 or x=x3 or x=x4 or x=x5 or x=x6 or x=x7 or x=x8 or x=x9 or x=x10
    or x=x1 iff x in {x2,x3,x4,x5,x6,x7,x8,x9,x10} or x = x1
      by ENUMSET1:def 7;
    hence x in {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} iff x in {x2,x3,x4,x5,x6,
    x7,x8,x9,x10} \/ {x1} by A1,ENUMSET1:def 8,XBOOLE_0:def 3;
  end;
  hence thesis by TARSKI:2;
end;
