let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st not x in still_not-bound_in p holds
(All x,(p => q)) => (p => (All x,q)) is valid
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in p implies (All x,(p => q)) => (p => (All x,q)) is valid )
assume not x in still_not-bound_in p ; :: thesis: (All x,(p => q)) => (p => (All x,q)) is valid
then A1: p => (All x,p) is valid by Th27;
(All x,(p => q)) => ((All x,p) => (All x,q)) is valid by Th34;
then (All x,p) => ((All x,(p => q)) => (All x,q)) is valid by LUKASI_1:48;
then p => ((All x,(p => q)) => (All x,q)) is valid by A1, LUKASI_1:43;
hence (All x,(p => q)) => (p => (All x,q)) is valid by LUKASI_1:48; :: thesis: verum