let R be Relation; :: thesis: ( R is being_partial-order implies R ~ is being_partial-order )
assume ( R is reflexive & R is transitive & R is antisymmetric ) ; :: according to ORDERS_1:def 4 :: thesis: R ~ is being_partial-order
hence ( R ~ is reflexive & R ~ is transitive & R ~ is antisymmetric ) by RELAT_2:27, RELAT_2:40, RELAT_2:42; :: according to ORDERS_1:def 4 :: thesis: verum