The law sounds like: p implies that q implies that p and q. And the task is to prove that using just two first axioms of PL plus the Novikov's axiom (p⊃q)⊃((p⊃r)⊃(p⊃q&r)),that means that any formulations you can achieve by deriving them from p, you can conjunct them together, we can get the given formula.
(i) p⊃(q⊃p) (ii) (p⊃(q⊃r))⊃((p⊃q)⊃(p⊃r)) (iii) (p⊃q)⊃((p⊃r)⊃(p⊃q&r))
Hence, this proves that in the previous proof of the law of transportation instead of this axiom the Novikov's axiom may be used, that means that both of ways to prove the law of transportation is possible.
Last Edit: Feb 23, 2021 21:56:28 GMT by Eugene 2.0