Mathematical Logic: "For all" and "There exists"?

Question

I am asked to show that:
|-- (Ax)(A --> (B = C)) --> ((Ax)(A --> B) = (Ax)(A --> C))

Note: (Ax), the A is supposed to be upsidown.

I could solve this if the (Ax) wasn't there, but it is, and it's throwing me off. I know what it means, but what's the difference in terms of solving? Can I just pretend it's not there, and solve anyway?

Answer 1

Pretty much. As long as your solution is valid no matter the value of x -- well, then it's valid for all x!