Which of the following is a valid first order formula ?
(Here $α$ and $β$ are first order formula with $x$ as their only free variable)
- $[((∀x)[α] ⇒ (∀x)[β])] ⇒ [(∀x)[α ⇒ β]]$
- $[(∀x)[α]] ⇒ [(∃x)[α ∧ β]]$
- $[((∀x)[α ∨ β] ⇒ (∃x)[α])] ⇒ [(∀x)[α]]$
- $[(∀x)[α ⇒ β]] ⇒ [((∀x)[α]) ⇒ (∀x)[β])]$
I tried by taking $α$ as $0=0$ and $β$ as $0=1$, but still not getting.
Is there something that I am missing ?