Proving $\forall x \forall y Rxy \therefore \forall x \forall y Ryx$.

Question

I have been having a hard time trying to understand how to prove the following proof:

$\forall x \forall y Rxy \therefore \forall x \forall y Ryx$

What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.

Answer 1

What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...

What you hav to do is :

1) $∀x∀yRxy$

2) $∀yRay$ --- by UI

3) $Rab$ --- by UI

4) $∀yRyb$ --- by UG

5) $∀x∀yRyx$ --- by UG.