Overloading cast to bool enables casting to int

Question

Consider following class used to wrap enum

class A {
    int v;
    A(int v) : v(v) { }
public:
    enum B : int { X = 1, Y = 2, Z = 3 };
    A(B v) : A(static_cast<int>(v)) { }
    A operator|(const A &b) const { return v | b.v; }
    operator bool() const { return v; }
};

int main() {
    A a(A::Y);
    if (a) 
        return 1;
    a = a | A::X; // this line failes to compile
    return 0;
}

I get an error on the marked line about ambigous overload

1.cpp:15:11: note: candidates are:
1.cpp:15:11: note: operator|(int, int) <built-in>
1.cpp:7:7: note: A A::operator|(const A&) const

If i comment out the bool cast operator the ambigous overload error goes away, so I suggest ambiguity arose from following casting path

(A)a -[operator]-> (bool)a -[implicit?]-> (int)a

Is there a way to resolve this ambiguity? The bool operator is used to allow

if (a) ...

and I'd rather stick to it than use something like

if (!!a) ...

with operator!().