let X be Subset of MC-wff; :: thesis: X c= CnS4 X
let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in X or a in CnS4 X )
assume A1: a in X ; :: thesis: a in CnS4 X
then reconsider t = a as Element of MC-wff ;
for T being Subset of MC-wff st T is S4_theory & X c= T holds
t in T by A1;
hence a in CnS4 X by Def23; :: thesis: verum