Hi,

I have used the semantic tableau procedure to check if the following sequent is valid. I get the answer that it is valid, however I am not sure if it is indeed valid and I havent made an error while writing the tableau. I havent included the tableau in this post as I don't know how to include it but the sequent is the following:

$\displaystyle

(\exists x A(x)) \rightarrow B \vdash \forall x (A(x) \rightarrow B)

$

Is this sequent indeed valid?

Another sequent:

$\displaystyle

(\forall x A(x)) \rightarrow B \vdash \exists x (A(x) \rightarrow B)

$

Also for this 2nd sequent I get the result that it is valid.

Am I correct for both sequents?

Thanks for any help.