let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x being bound_QC-variable of A st not x in still_not-bound_in p holds
p => (All (x,p)) is valid
let p 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
p => (All (x,p)) is valid
let x be bound_QC-variable of A; :: thesis: ( not x in still_not-bound_in p implies p => (All (x,p)) is valid )
A1: p => p is valid ;
assume not x in still_not-bound_in p ; :: thesis: p => (All (x,p)) is valid
hence p => (All (x,p)) is valid by A1, CQC_THE1:67; :: thesis: verum