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

for p, q being Element of CQC-WFF Al holds (p '&' q) => (q '&' p) in Cn X

let X be Subset of (CQC-WFF Al); :: thesis: for p, q being Element of CQC-WFF Al holds (p '&' q) => (q '&' p) in Cn X

let p, q be Element of CQC-WFF Al; :: thesis: (p '&' q) => (q '&' p) in Cn X

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

(p '&' q) => (q '&' p) in T ;

hence (p '&' q) => (q '&' p) in Cn X by Def2; :: thesis: verum

for p, q being Element of CQC-WFF Al holds (p '&' q) => (q '&' p) in Cn X

let X be Subset of (CQC-WFF Al); :: thesis: for p, q being Element of CQC-WFF Al holds (p '&' q) => (q '&' p) in Cn X

let p, q be Element of CQC-WFF Al; :: thesis: (p '&' q) => (q '&' p) in Cn X

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

(p '&' q) => (q '&' p) in T ;

hence (p '&' q) => (q '&' p) in Cn X by Def2; :: thesis: verum