let p be Element of CQC-WFF ; :: thesis: for x, y being bound_QC-variable 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; :: 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 Th18;
hence (Ex (x,p)) => (Ex (y,p)) is valid by A1, Th22; :: thesis: verum