theorem Th123: :: Introduction 'or' to premiss, No.2
  (X \/ {p} |-_IPC r & X \/ {q} |-_IPC r) implies X \/ {p 'or' q} |-_IPC r
proof
  set U = p 'or' q;
  assume A1: (X \/ {p} |-_IPC r & X \/ {q} |-_IPC r); then
A2: X |-_IPC p => r by Th53;
A3: X |-_IPC q => r by A1,Th53;
  X |-_IPC (p => r) => ((q => r) => (U => r)) by Th25; then
  X |-_IPC (q => r) => (U => r) by A2,Th27; then
A6: X |-_IPC U => r by A3,Th27;
A7: {U} |-_IPC U by Th65;
    {U} c= X \/ {U} by XBOOLE_1:7; then
A11: X \/ {U} |-_IPC U by A7,Th66;
   X c= X \/ {U} by XBOOLE_1:7; then
  X \/ {U} |-_IPC U => r by A6,Th66;
  hence thesis by A11,Th27;
end;
