Section 2.4: Problem 4 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

Give a deduction (from $\emptyset$ ) of $\forall x\phi\rightarrow\exists x\phi$ . (Note that you should not merely prove that such a deduction exists. You are instead asked to write out the entire deduction.)

$<\overset{1:A2}{\forall x\phi\rightarrow\phi}$ ,

Note: a few last steps of the example on pages 119-120 provides an alternative approach to this problem, which is more generally applicable, however, seems to lead to a longer deduction.

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Section 2.4: Problem 4 Solution

Section 2.4: Problem 4 Solution