let T, X be Subset of CQC-WFF ; :: thesis: ( T is being_a_theory & X c= T implies Cn X c= T )
assume that
A1: T is being_a_theory and
A2: 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, A2, Def2; :: thesis: verum

end;