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

( 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