reserve T, X, Y for Subset of MC-wff;
reserve p, q, r, s for Element of MC-wff;

theorem Th38:
  ( r => p ) => (( r => q ) => ( r => ( p '&' q ))) in IPC-Taut
proof
A1: ( r => ( q => ( p '&' q ))) => (( r => q ) => ( r => ( p '&' q ))) in
  IPC-Taut by Def14;
  p => ( q => ( p '&' q )) in IPC-Taut by Def14;
  then
A2: r => ( p => ( q => ( p '&' q ))) in IPC-Taut by Th18;
  (r => ( p => ( q => ( p '&' q )))) => (( r => p ) => ( r => ( q => ( p
  '&' q )))) in IPC-Taut by Def14;
  then ( r => p ) => ( r => ( q => ( p '&' q ))) in IPC-Taut by A2,Def14;
  hence thesis by A1,Th26;
end;
