C++ is operator!= automatically provided when operator== defined

No, operators (apart from assignment) are never automatically generated. It's easy enough to define it in terms of ==:

bool operator!=(A const & l, A const & r) {return !(l == r);}

The operator != is not automatically provided for you. You may want to read about rel_ops namespace if you want such automation. Essentially you can say

using namespace std::rel_ops;

before using operator !=.

What you're after isn't provided by the language for obvious reasons. What you want is provided for by boost::operators:

class MyClass : boost::operators<MyClass> {
    bool operator==(const MyInt& x) const;
}

will get you an operator!=() based on your operator==()