let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x, y being bound_QC-variable of A st not y in still_not-bound_in p holds
(All (x,p)) => (All (y,p)) is valid
let p be Element of CQC-WFF A; :: thesis: for x, y being bound_QC-variable of A st not y in still_not-bound_in p holds
(All (x,p)) => (All (y,p)) is valid
let x, y be bound_QC-variable of A; :: thesis: ( not y in still_not-bound_in p implies (All (x,p)) => (All (y,p)) is valid )
assume not y in still_not-bound_in p ; :: thesis: (All (x,p)) => (All (y,p)) is valid
then ( (All (x,p)) => p is valid & not y in still_not-bound_in (All (x,p)) ) by Th5, CQC_THE1:66;
hence (All (x,p)) => (All (y,p)) is valid by CQC_THE1:67; :: thesis: verum