 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 => to premiss, No.1
  (|-_IPC p) & ({r} |-_IPC q) implies {p => r} |-_IPC q
proof
A20: {} c= {p => r};
  assume
A1: (|-_IPC p) & ({r} |-_IPC q); then
A2: {p => r} |-_IPC p by A20,Th66;
   {p => r} |-_IPC p => r by Th65; then
A4: {p => r} |-_IPC r by A2,Th27;
   {r} c= {p => r} \/ {r} by XBOOLE_1:7; then
  {p => r} \/ {r} |-_IPC q by A1,Th66;
  hence thesis by A4,Th116;
end;
