# Section 2.4: Problem 10 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Show that
By the Generalization Theorem, it is sufficient to show that $\forall x\forall yPxy\vdash Pyx$ . By EAV, $\forall x\forall yPxy\vdash\forall x\forall zPxz$ . By axiom group 2, $\vdash\forall x\forall zPxz\rightarrow\forall zPyz$ and $\vdash\forall zPyz\rightarrow Pyx$ . By applying MP twice, we get $\forall x\forall yPxy\vdash Pyx$ .