Prove that $$((\forall x) ( a \Rightarrow b)) \Rightarrow [((\forall x)( a)) \Rightarrow ((\forall x) (b)) ]$$ is valid first order formula. Where ' a ' and 'b' are first order formulae.
My attempt: $(\forall x) (\neg a \lor b) \Rightarrow \exists x (\neg a \lor b) \Rightarrow \exists x (\neg a) \lor \exists x(b) \Rightarrow \neg(\forall x)(a) \lor \exists x(b) \Rightarrow \forall x (a) \Rightarrow \exists x (b)$
I am not able to get the RHS . What is wrong with this method?