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P v P Premise

~p Assumption

p Disjunctive Syllogism (1, 2)

p & ~p Conjunction (3, 4)

~p --> (p & ~p) Conditional Proof (2--4)

p v ~p EMI

~p v p Commutation (6)

~p v ~~p Double Negation (7)

~(p & ~p) De Morgan's (8)

~~p Modus Tollens (5, 9)

p Double Negation

My question is, how do I show p v p = p WITHOUT using a truth table OR a conditional prove? I can only use the basic rules of inference (Excluded Middle Introduction, Disjunctive Syllogism, Addition, Conjunction, Simplification) as well as the rules of replacement (De Morgan's, Distribution, etc.)