let Al be QC-alphabet ; :: thesis: for X being Subset of (CQC-WFF Al) holds X c= Cn X

let X be Subset of (CQC-WFF Al); :: thesis: X c= Cn X

let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in X or a in Cn X )

assume A1: a in X ; :: thesis: a in Cn X

then reconsider t = a as Element of CQC-WFF Al ;

for T being Subset of (CQC-WFF Al) st T is being_a_theory & X c= T holds

t in T by A1;

hence a in Cn X by Def2; :: thesis: verum

let X be Subset of (CQC-WFF Al); :: thesis: X c= Cn X

let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in X or a in Cn X )

assume A1: a in X ; :: thesis: a in Cn X

then reconsider t = a as Element of CQC-WFF Al ;

for T being Subset of (CQC-WFF Al) st T is being_a_theory & X c= T holds

t in T by A1;

hence a in Cn X by Def2; :: thesis: verum