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

for p being Element of CQC-WFF Al

for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

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

for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

let p be Element of CQC-WFF Al; :: thesis: for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

let x be bound_QC-variable of Al; :: thesis: (All (x,p)) => p in Cn X

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

(All (x,p)) => p in T ;

hence (All (x,p)) => p in Cn X by Def2; :: thesis: verum

for p being Element of CQC-WFF Al

for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

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

for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

let p be Element of CQC-WFF Al; :: thesis: for x being bound_QC-variable of Al holds (All (x,p)) => p in Cn X

let x be bound_QC-variable of Al; :: thesis: (All (x,p)) => p in Cn X

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

(All (x,p)) => p in T ;

hence (All (x,p)) => p in Cn X by Def2; :: thesis: verum