Let $x,y$ be variables, $A(x,y)$ a formula in which both $x$ and $y$ occur free.
Show that
$$\forall x \Big(\forall y\big(A(x,y)\big)\Big) \to \forall y \Big(\forall x\big(A(x,y)\big)\Big)$$
is logically valid
Let $x,y$ be variables, $A(x,y)$ a formula in which both $x$ and $y$ occur free.
Show that
$$\forall x \Big(\forall y\big(A(x,y)\big)\Big) \to \forall y \Big(\forall x\big(A(x,y)\big)\Big)$$
is logically valid