What is wrong with this proof? Theorem. 7 is divisible by 3 Proof. Every integer

Question

What is wrong with this proof?
Theorem. 7 is divisible by 3
Proof. Every integer number is divisible by 3 or it is not. Let c be an arbitrary integer number. Therefore, it is divisible by 3 or it is not. Suppose it is divisible by 3. By the rule of universal generalization, if an arbitrary number is divisible by 3, every number is is divisible by 3. Therefore, 7 is divisible by 3. What is wrong with this proof?
Theorem. 7 is divisible by 3
Proof. Every integer number is divisible by 3 or it is not. Let c be an arbitrary integer number. Therefore, it is divisible by 3 or it is not. Suppose it is divisible by 3. By the rule of universal generalization, if an arbitrary number is divisible by 3, every number is is divisible by 3. Therefore, 7 is divisible by 3. What is wrong with this proof?
Theorem. 7 is divisible by 3
Proof. Every integer number is divisible by 3 or it is not. Let c be an arbitrary integer number. Therefore, it is divisible by 3 or it is not. Suppose it is divisible by 3. By the rule of universal generalization, if an arbitrary number is divisible by 3, every number is is divisible by 3. Therefore, 7 is divisible by 3.

Explanation / Answer

Since rule of universal generalisation works if for arbitrary c , P(c) is true then for all x P(x) is true. But here you assume that c is divisible by 3. You can’t suppose c is divisible by 3. First you have to show that for arbitrary c , c is divisible by 3. Then you can use universal Generalization.

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