let A be QC-alphabet ; :: thesis: for H being Element of QC-WFF A st H is universal holds
the_scope_of H is_proper_subformula_of H
let H be Element of QC-WFF A; :: thesis: ( H is universal implies the_scope_of H is_proper_subformula_of H )
assume H is universal ; :: thesis: the_scope_of H is_proper_subformula_of H
then the_scope_of H is_immediate_constituent_of H by Th50;
hence the_scope_of H is_proper_subformula_of H by Th53; :: thesis: verum