Finite set of primes

There is a finite set $$\{p_1, \ldots, p_r\}$$ of all primes $$\Rightarrow$$ Contradiction

Explanation

Is $$n = p_1 p_2 \cdots p_r + 1 $$ prime?


 * Yes, n is prime $$\Rightarrow$$ Contradiction. (*)


 * No, n is not prime $$\Rightarrow$$ Contradiction. (more)