In D. Scott: More on the axiom of extensionality, in Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary, edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for The Hebrew University of Jerusalem, Magnes Press, Jerusalem 1961, pp. 115--131, Dana Scott introduces a system $ZF^s$: Let $R^s$ be replacement with coextensionality in place of identity. $ZF^s$ is $ZF$ minus extensionality, with $R^s$ instead of ordinary replacement. Scott shows that $ZF^s$ interprets ZF.

How may we show that $ZF^s$ proves that the transitive closure of any set is as well a set?

In D. Scott: More on the axiom of extensionality, in Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary, edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for The Hebrew University of Jerusalem, Magnes Press, Jerusalem 1961, pp. 115--131, Dana Scott introduces a system $ZF^s$: Let $R^s$ be replacement with coextensionality in place of identity. $ZF^s$ is $ZF$ minus extensionality, with $R^s$ instead of ordinary replacement. Scott shows that $ZF^s$ interprets ZF.

May we show that $ZF^s$ proves that the transitive closure of any set is as well a set, without invoking the interpretation?