let T, X be Subset of MC-wff; :: thesis: ( T is S4_theory & X c= T implies CnS4 X c= T )
assume that
A1: T is S4_theory and
A2: X c= T ; :: thesis: CnS4 X c= T
let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in CnS4 X or a in T )
thus ( not a in CnS4 X or a in T ) by A1, A2, Def23; :: thesis: verum