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;
