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 x in still_not-bound_in p holds
(Ex (x,p)) => (Ex (y,p)) is valid
let p be Element of CQC-WFF A; :: thesis: for x, y being bound_QC-variable of A st not x in still_not-bound_in p holds
(Ex (x,p)) => (Ex (y,p)) is valid
let x, y be bound_QC-variable of A; :: thesis: ( not x in still_not-bound_in p implies (Ex (x,p)) => (Ex (y,p)) is valid )
assume not x in still_not-bound_in p ; :: thesis: (Ex (x,p)) => (Ex (y,p)) is valid
then A1: not x in still_not-bound_in (Ex (y,p)) by Th6;
p => (Ex (y,p)) is valid by Th15;
hence (Ex (x,p)) => (Ex (y,p)) is valid by A1, Th19; :: thesis: verum