Now consider a propositional function Fx in which the variable argument x is itself a propositional function.
Call it a propositional function; and, if 4)x be a propositional function, the undetermined variable x is the argument.
Two propositional functions 4)x and fix are "extensionally identical" if any determination of x in 4)x which converts 4)x into a true proposition also converts 4'x into a true proposition, and conversely for 4' and 4).
If Fx is true when, and only when, x is determined to be either 4) or some other propositional function extensionally equivalent to (A, then the proposition F4 is of the form which is ordinarily recognized as being about the class determined by )x taken in extension - that is, the class of entities for which 4)x is a true proposition when x is determined to be any one of them.
A similar theory holds for relations which arise from the consideration of propositional functions with two or more variable arguments.