let T, X be Subset of HP-WFF; :: thesis: ( T is Hilbert_theory & X c= T implies CnPos X c= T )
assume that
A1: T is Hilbert_theory and
A2: X c= T ; :: thesis: CnPos X c= T
let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in CnPos X or a in T )
thus ( not a in CnPos X or a in T ) by A1, A2, Def11; :: thesis: verum