let p be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st not x in still_not-bound_in p holds
(Ex (x,p)) => p is valid
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in p implies (Ex (x,p)) => p is valid )
A1: p => p is valid ;
assume not x in still_not-bound_in p ; :: thesis: (Ex (x,p)) => p is valid
hence (Ex (x,p)) => p is valid by A1, Th22; :: thesis: verum