let A be QC-alphabet ; :: thesis: for F, H being Element of QC-WFF A st H is universal holds
( F is_immediate_constituent_of H iff F = the_scope_of H )
let F, H be Element of QC-WFF A; :: thesis: ( H is universal implies ( F is_immediate_constituent_of H iff F = the_scope_of H ) )
assume H is universal ; :: thesis: ( F is_immediate_constituent_of H iff F = the_scope_of H )
then H = All ((bound_in H),(the_scope_of H)) by Th6;
hence ( F is_immediate_constituent_of H iff F = the_scope_of H ) by Th46; :: thesis: verum