in First order logic, Want to show ¬∃x (∀zQxz →Qcy) ⊢ ∀x∀z Qtz

37 Views Asked by At

Want to show $ ¬∃x (∀ z Q_x,_z →Q_c,_y) ⊢ ∀x∀zQ_t,_z $

and Q is binary, z does not occur in t

I did just basic one..

ETS : ⊢$ ∀x ¬(∀ z Q_x,_z →Q_c,_y) → ∀x∀zQ_t,_z $
ETS : ⊢$ ∀x ( ¬(∀ z Q_x,_z →Q_c,_y) → ∀zQ_t,_z )$

What can I further do..? Maybe I can apply Genralization or Specification. Because z odes not occur in t

I am sorry for a too basic Question.