let Al be QC-alphabet ; :: thesis: for p being Element of CQC-WFF Al
for x being bound_QC-variable of Al
for Sub being CQC_Substitution of Al st not x in rng (RestrictSub (x,(All (x,p)),Sub)) holds
S_Bound [(All (x,p)),Sub] = x

let p be Element of CQC-WFF Al; :: thesis: for x being bound_QC-variable of Al
for Sub being CQC_Substitution of Al st not x in rng (RestrictSub (x,(All (x,p)),Sub)) holds
S_Bound [(All (x,p)),Sub] = x

let x be bound_QC-variable of Al; :: thesis: for Sub being CQC_Substitution of Al st not x in rng (RestrictSub (x,(All (x,p)),Sub)) holds
S_Bound [(All (x,p)),Sub] = x

let Sub be CQC_Substitution of Al; :: thesis: ( not x in rng (RestrictSub (x,(All (x,p)),Sub)) implies S_Bound [(All (x,p)),Sub] = x )
set finSub = RestrictSub (x,(All (x,p)),Sub);
set S = [(All (x,p)),Sub];
assume A1: not x in rng (RestrictSub (x,(All (x,p)),Sub)) ; :: thesis: S_Bound [(All (x,p)),Sub] = x
reconsider q = [(All (x,p)),Sub] `1 as Element of CQC-WFF Al ;
( [(All (x,p)),Sub] `2 = Sub & bound_in q = x ) by QC_LANG2:7;
hence S_Bound [(All (x,p)),Sub] = x by ; :: thesis: verum