let T, X be Subset of CQC-WFF; :: thesis: ( T is being_a_theory & X c= T implies Cn X c= T )
assume A1: ( T is being_a_theory & X c= T ) ; :: thesis: Cn X c= T
thus Cn X c= T :: thesis: verum

proof

let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in Cn X or a in T )
assume a in Cn X ; :: thesis: a in T
hence a in T by A1, Def2; :: thesis: verum

end;