theorem Th30: :: SUBLEMMA:30

for Al being QC-alphabet
for x being bound_QC-variable of Al
for S being Element of CQC-Sub-WFF Al
for xSQ being second_Q_comp of [S,x] st [S,x] is quantifiable holds
( CQCSub_the_scope_of (CQCSub_All ([S,x],xSQ)) = S & CQCQuant ((CQCSub_All ([S,x],xSQ)),(CQC_Sub (CQCSub_the_scope_of (CQCSub_All ([S,x],xSQ))))) = CQCQuant ((CQCSub_All ([S,x],xSQ)),(CQC_Sub S)) )