User blog comment:Emlightened/Little Bigeddon/@comment-35470197-20181017073031

The second and third lines of the axiom on \(T\) look strange, because for any \(d \in c\), there should be at most one \(e\) with \(\exists ! f(d = \langle e, \rangle)\). What is the correct formula?

Also, \(\ulcorner d = e \urcorner\) in the fourth line seems to be a typo of \(\ulcorner x_d = x_e \urcorner\).

Then what does \(c(d)\) in the fourth line mean? I guess that it is a typo of \(x_d\), which is irrelevant to \(c\).

In addition, could you tell me axioms other than that of \(T\)? Is it the axiom of \(\textrm{ZFC}\) whose separation and replacement axiom schema refer to any formulae (allowing the occurrence of \(T\)), right?