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