let A be QC-alphabet ; :: thesis: for H being Element of QC-WFF A st H is conjunctive holds
( the_left_argument_of H is_proper_subformula_of H & the_right_argument_of H is_proper_subformula_of H )
let H be Element of QC-WFF A; :: thesis: ( H is conjunctive implies ( the_left_argument_of H is_proper_subformula_of H & the_right_argument_of H is_proper_subformula_of H ) )
assume H is conjunctive ; :: thesis: ( the_left_argument_of H is_proper_subformula_of H & the_right_argument_of H is_proper_subformula_of H )
then ( the_left_argument_of H is_immediate_constituent_of H & the_right_argument_of H is_immediate_constituent_of H ) by Th49;
hence ( the_left_argument_of H is_proper_subformula_of H & the_right_argument_of H is_proper_subformula_of H ) by Th53; :: thesis: verum