how we can prove that argument $P_1,P_2,...,P_n $?

Question

I ran into a one claims on LOGIC. how can add more direction or hint to me?

if we have an argument $P_1,P_2,...,P_n $ such that $ n>3$ ($p_i$ is premise) why $P_1,P_2,....,P_n,P_1$ is necessarily be an argument?

Answer 1

Assuming I understood your question correctly:

Let $p,q$ be two propositions, then according to the simplification rule the proposition $(p\wedge q) \to p$ is a tautology. Therefore, $(p\wedge q) \Rightarrow p$ is a valid argument.

You can prove this rule using truth-tables, and then extend it to any finite number of propositions $p_i$ (induction).