I was going through this guide on operator overloading in C++.

If I try to implement all the comparison operators using the <=> operator:

friend auto operator<=>(const Some_class& lhs, const Some_class& rhs)
{
      if (lhs.x < rhs.x) return std::strong_ordering::less;
      if (lhs.x > rhs.x) return std::strong_ordering::greater;   
      else return std::strong_ordering::equal;
}

The == operator wont the defined for Some_class. So I additionally have to implement:

friend bool operator==(const Some_class& lhs, const Some_class& rhs)
{
      if (lhs.x == rhs.x) return true;
      return false;
}

The guide does state that this is necessary:

In C++20, if a comparison isn’t directly implemented, the compiler
will also try to use rewrite candidates. Thanks to this, even if <=>
isn’t defaulted (which would implement all operators), we only have to
implement == and <=>, and all other comparisons are rewritten in terms
of these two.

But I don’t get why. Why is not the first code snippet enough for the compiler to define the == operator?

Note: I can not default <=> in this case.