theorem Th53: :: SUBLEMMA:53

for Al being QC-alphabet
for x being bound_QC-variable of Al
for A being non empty set
for v being Element of Valuations_in (Al,A)
for S being Element of CQC-Sub-WFF Al
for xSQ being second_Q_comp of [S,x] st [S,x] is quantifiable holds
for a being Element of A holds
( Val_S ((v . ((S_Bound (@ (CQCSub_All ([S,x],xSQ)))) | a)),S) = (NEx_Val ((v . ((S_Bound (@ (CQCSub_All ([S,x],xSQ)))) | a)),S,x,xSQ)) +* (x | a) & dom (RestrictSub (x,(All (x,(S `1))),xSQ)) misses {x} )