let R be Relation; :: thesis: ( R is being_quasi-order implies R ~ is being_quasi-order )
assume ( R is reflexive & R is transitive ) ; :: according to ORDERS_1:def 3 :: thesis: R ~ is being_quasi-order
hence ( R ~ is reflexive & R ~ is transitive ) by RELAT_2:27, RELAT_2:42; :: according to ORDERS_1:def 3 :: thesis: verum