Default constructor prevents from calling emplace_back

It seems that adding a default constructor prevents from calling emplace_back and produces the error message: "static assertion failed: type is not assignable" (gcc 5.3 with -std=c++14). Here is a simple code that illustrates the issue:

class A {
public:
    int a;
    A() = default;
    A(int a) {
        this->a = a;
    }
    A(A const & a) = delete;
    A& operator =(A const & a) = delete;
    A(A && a) = default;
    A& operator =(A && a) = default;
};

int main() {

    A a(4);
    std::vector<A> vec;
    vec.emplace_back(std::move(a)); // Error: type is not assignable
    return 0;
}

When removing the default constructor, the error goes away! Is this normal behaviour on part of the compiler or is it a bug?