How does one prove that
(P ∨ Q) ∧ (P ∨ R) ⊢ P ∨ (Q ∧ R)
Is this a well formed proof?
(P ∨ Q) ∧ (P ∨ R) (premise) (P ∨ Q) (P ∨ R) (and-elimination) ~P-> Q ~P-> R (???) ~P (assumption) Q R (Modus Ponens) Q ∧ R (and-introduction) ~P -> (Q ∧ R) (conditional proof, discarding assumption ~P) P ∨ (Q ∧ R) (???)
How are you supposed to do it otherwise?
EDIT: The first answer to this question does use this equivalence: Proof of the distributive law in implication
Is it something that's acceptable in propositional logic?