 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 Th77:
  |-_IPC ((p => r) '&' (q => r)) => ((p 'or' q) => r)
proof
  set X = {(p => r) '&' (q => r)};
A1: X |-_IPC p => r by Th73;
A2: X |-_IPC q => r by Th74;
  X |-_IPC (p => r) => ((q => r) => ((p 'or' q) => r)) by Th25; then
  X |-_IPC (q => r) => ((p 'or' q) => r) by A1,Th27; then
  X |-_IPC (p 'or' q) => r by A2,Th27;
  hence thesis by Th54;
end;
