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applying Sjf assertion AxIII AxIII(b3 AxIII(c2 Axiomatic Set Theory axioms AxIV Axl(a class admitted class defined class of k-tuplets class of normal class of ordinals class of pairs class so defined Class Theorem CLASSES AND FINITE Cranberry Township CTc(i DbFnc definition df the class Df.A Df.B Df.C existence theorem existential quantification F F F false proposition finite class finite sets formula representing given class Greek iteration of F Lemma Let the class logical constants mathematics matrix Mozart Mz e G one-to-one correspondence ordered pairs Paul Bernays Peano Axioms Proof Analogous Proof Immediate proper sub-class propositional function rebracketing represented as follows representing a false representing a true result of applying self-augment set theory standard expression sub-proof c(ii symbol THEORY OF FINITE tion transitive set true proposition tuplets x e Ml