let Al be QC-alphabet ; :: thesis: for Sub being CQC_Substitution of Al ex S being Element of CQC-Sub-WFF Al st
( S `1 = VERUM Al & S `2 = Sub )
let Sub be CQC_Substitution of Al; :: thesis: ex S being Element of CQC-Sub-WFF Al st
( S `1 = VERUM Al & S `2 = Sub )
VERUM Al = <*[0,0]*> by QC_LANG1:def 14;
then reconsider S = [(VERUM Al),Sub] as Element of QC-Sub-WFF Al by SUBSTUT1:def 16;
take S ; :: thesis: ( S is Element of CQC-Sub-WFF Al & S `1 = VERUM Al & S `2 = Sub )
set X = { G where G is Element of QC-Sub-WFF Al : G `1 is Element of CQC-WFF Al } ;
{ G where G is Element of QC-Sub-WFF Al : G `1 is Element of CQC-WFF Al } = CQC-Sub-WFF Al by SUBSTUT1:def 39;
then A1: for G being Element of QC-Sub-WFF Al st G `1 is Element of CQC-WFF Al holds
G in CQC-Sub-WFF Al ;
S `1 = VERUM Al ;
then reconsider S = S as Element of CQC-Sub-WFF Al by A1;
S `2 = Sub ;
hence ( S is Element of CQC-Sub-WFF Al & S `1 = VERUM Al & S `2 = Sub ) ; :: thesis: verum