let Al be QC-alphabet ; :: thesis: for X being Subset of (CQC-WFF Al)

for p being Element of CQC-WFF Al holds (('not' p) => p) => p in Cn X

let X be Subset of (CQC-WFF Al); :: thesis: for p being Element of CQC-WFF Al holds (('not' p) => p) => p in Cn X

let p be Element of CQC-WFF Al; :: thesis: (('not' p) => p) => p in Cn X

for T being Subset of (CQC-WFF Al) st T is being_a_theory & X c= T holds

(('not' p) => p) => p in T ;

hence (('not' p) => p) => p in Cn X by Def2; :: thesis: verum

for p being Element of CQC-WFF Al holds (('not' p) => p) => p in Cn X

let X be Subset of (CQC-WFF Al); :: thesis: for p being Element of CQC-WFF Al holds (('not' p) => p) => p in Cn X

let p be Element of CQC-WFF Al; :: thesis: (('not' p) => p) => p in Cn X

for T being Subset of (CQC-WFF Al) st T is being_a_theory & X c= T holds

(('not' p) => p) => p in T ;

hence (('not' p) => p) => p in Cn X by Def2; :: thesis: verum