Assembly of a slidable wall part, such as a French door or a sliding door, and an operating device, comprising: - one or more carriages which are arranged on an underside of the slidable wall part and which define a first, lying direction; - an operating rod connected to the one or more carriages and extending in a second direction, wherein the second direction extends substantially transversely of the first direction, wherein said operating rod is configured to displace the carriages between a rest position, in which the slidable wall part rests on a ground surface, and an operative position in which the slidable wall part is lifted by the carriages and is displaceable thereby; - wherein a transmission unit is provided in line with the operating rod, which unit is connected via a driving connection to a drive, and wherein the driving connection extends substantially in a third direction parallel to the first direction; - wherein the transmission unit comprises a rod mechanism configured to convert a tensile or pressure force applied by the driving connection in the third direction to a tensile or pressure force directed in the second direction, wherein the rod mechanism of the transmission unit is a four-rod mechanism, comprising: - a guide rail which is arranged on the slidable wall part in the third direction; - a first rod which is guided by the guide rail and is slidable relative thereto in a longitudinal direction of the guide rail; - a second rod which is arranged pivotally between the first rod and a third rod; - wherein the third rod comprises a rocker that is arranged substantially on or in line with the longitudinal direction of the guide rail for pivoting around a fixed pivot shaft that is fixed on the slideable wall part; - wherein the second rod and the third rod are connected via a pivot shaft; - wherein the slidable wall part forms a fourth rod of the four-rod mechanism, characterized in that the third rod comprises a further pivot shaft that is connected to the operating rod; - wherein a distance between the fixed pivot shaft and the pivot shaft is greater than a distance between the fixed pivot shaft and the further pivot shaft; and - wherein the driving connection comprises a spindle which can be driven with the drive and which is configured to displace the first rod in longitudinal direction relative to the guide rail. - one or more carriages which are arranged on an underside of the slidable wall part and which define a first, lying direction; - an operating rod connected to the one or more carriages and extending in a second direction, wherein the second direction extends substantially transversely of the first direction, wherein said operating rod is configured to displace the carriages between a rest position, in which the slidable wall part rests on a ground surface, and an operative position in which the slidable wall part is lifted by the carriages and is displaceable thereby; - wherein a transmission unit is provided in line with the operating rod, which unit is connected via a driving connection to a drive, and wherein the driving connection extends substantially in a third direction parallel to the first direction; - wherein the transmission unit comprises a rod mechanism configured to convert a tensile or pressure force applied by the driving connection in the third direction to a tensile or pressure force directed in the second direction, - a guide rail which is arranged on the slidable wall part in the third direction; - a first rod which is guided by the guide rail and is slidable relative thereto in a longitudinal direction of the guide rail; - a second rod which is arranged pivotally between the first rod and a third rod; - wherein the third rod comprises a rocker that is arranged substantially on or in line with the longitudinal direction of the guide rail for pivoting around a fixed pivot shaft that is fixed on the slideable wall part; - wherein the second rod and the third rod are connected via a pivot shaft; - wherein the slidable wall part forms a fourth rod of the four-rod mechanism, characterized in that the third rod comprises a further pivot shaft that is connected to the operating rod; - wherein a distance between the fixed pivot shaft and the pivot shaft is greater than a distance between the fixed pivot shaft and the further pivot shaft; and - wherein the driving connection comprises a spindle which can be driven with the drive and which is configured to displace the first rod in longitudinal direction relative to the guide rail.