 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 :: Introduction 'or' to premiss, No.1
  ({p} |-_IPC r & {q} |-_IPC r) implies {p 'or' q} |-_IPC r
proof
  set U = p 'or' q;
  set X = {U};
A2: |-_IPC (p => r) => ((q => r) => (U => r)) by Th35;
  assume
A1: {p} |-_IPC r & {q} |-_IPC r; then
A5: |-_IPC q => r by Th54;
   |-_IPC p => r by A1,Th54; then
   |-_IPC (q => r) => (U => r) by A2,Th37; then
A7: |-_IPC U => r by A5,Th37;
  {} c= X; then
  X |-_IPC U => r by A7,Th66;
  hence thesis by Th27,Th65;
end;
