Passable no-go device for downhole valve

A downhole valve has a flow tube (20) hydraulically actuated to open and close a flapper. The flow tube moved to a first position closes the flapper to restrict flow through the valve. The flow tube moved to a second position opens the flapper. A passable no-go device (50) disposed in the valve permits or restricts mechanical passage through the valve in response to the position of the flow tube. The apparatus has a support and one or more dogs (80) supported in windows (72) of the support and biased by springs. The flow tube in the first position pushes the dogs to an extended position that restricts mechanical passage through valve so that a tool cannot be passed through the valve while the flapper is closed. When the flow tube is in the second position, however, the dogs retract so the tool can be passed through the valve while the flapper is open.