How template influence implicitly-declared-rules in C++?

Example:

template<class T> class A{
  public:
    A(){}
    template<class U> A(A<U> &){}
  private:
    template<class U> A(A<U>&&){}
};

int main() {
  A<int> a1;// legal
  A<int> a2(std::move(a1));//legal. it calls implicitly-declared constructor.
}

but when I delete A(){}:

template<class T> class A{
  public:

    template<class U> A(A<U> &){}
  private:
    template<class U> A(A<U>&&){}
};

int main() {
  A<int> a1;// illegal. 3
  A<int> a2(std::move(a1));
}

---

• If template constructors didn't influence implicitly-declared-rules. why it becomes illegal?
• If template constructors influence implicitly-declared-rules, but why "A a2(std::move(a1));" legal?