 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
 |-_IPC (p =>(q 'or' (p => r))) => (p =>(q 'or' r))
proof
  set V = q 'or' r;
A1: {r} |-_IPC q 'or' r by Th121;
    {r} c= {p} \/ {r} by XBOOLE_1:7; then
A3: {p} \/ {r} |-_IPC V by A1,Th66;
A4: {p} |-_IPC p by Th65; then
A5: {p} \/ {p => r} |-_IPC V by A3,Th119;
A7: {q} |-_IPC V by Th120;
    {q} c= {p} \/ {q} by XBOOLE_1:7; then
    {p} \/ {q} |-_IPC V by A7,Th66; then
    {p} \/ {q 'or' (p => r)} |-_IPC V by A5,Th123; then
  {p} \/ {p => (q 'or' (p => r))} |-_IPC V by A4,Th119; then
  {p => (q 'or' (p => r))} |-_IPC p => V by Th53;
  hence thesis by Th54;
end;
