let X be Subset of MC-wff; :: thesis: X c= CnCPC X
let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in X or a in CnCPC X )
assume A1: a in X ; :: thesis: a in CnCPC X
then reconsider t = a as Element of MC-wff ;
for T being Subset of MC-wff st T is CPC_theory & X c= T holds
t in T by A1;
hence a in CnCPC X by Def20; :: thesis: verum