let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st not x in still_not-bound_in p holds
(All (x,(p => q))) => (p => (All (x,q))) is valid
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A 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 of A; :: 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 Th24;
(All (x,(p => q))) => ((All (x,p)) => (All (x,q))) is valid by Th30;
then (All (x,p)) => ((All (x,(p => q))) => (All (x,q))) is valid by LUKASI_1:44;
then p => ((All (x,(p => q))) => (All (x,q))) is valid by A1, LUKASI_1:42;
hence (All (x,(p => q))) => (p => (All (x,q))) is valid by LUKASI_1:44; :: thesis: verum