Would this class have a Strict Weak Ordering

Say I had class/struct Foo

struct Foo {
    int a, b;
    bool operator< (Foo const& r){
        return a < r.a;
    }
    bool operator== (Foo const& r){
        return a==r.a&&b==r.b;
    }
};
Foo bar = { 5, 1 };
Foo baz = { 5, 2 };

Now bar == baz is false but so are bar < baz and baz < bar.

Note that here the ordering completely ignores b but b is part of the equality relation.