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 & Ex (x,p) is valid holds
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 & Ex (x,p) is valid holds
p is valid
let x be bound_QC-variable of A; :: thesis: ( not x in still_not-bound_in p & Ex (x,p) is valid implies p is valid )
assume that
A1: not x in still_not-bound_in p and
A2: Ex (x,p) is valid ; :: thesis: p is valid
(Ex (x,p)) => p is valid by A1, Th20;
hence p is valid by A2, CQC_THE1:65; :: thesis: verum