subtle C++ inheritance error with protected fields

Below is a subtle example of accessing an instance's protected field x. B is a subclass of A so any variable of type B is also of type A. Why can B::foo() access b's x field, but not a's x field?

class A {
protected:
  int x;
};

class B : public A {
protected:
  A *a;
  B *b;
public:
  void foo() {
    int u = x;     // OK : accessing inherited protected field x
    int v = b->x;  // OK : accessing b's protected field x
    int w = a->x;  // ERROR : accessing a's protected field x
  }
};

Here is the error I get with g++

$ g++ -c A.cpp
A.cpp: In member function ‘void B::foo()’:
A.cpp:3: error: ‘int A::x’ is protected
A.cpp:14: error: within this context