Is there any way to look up in HashSet by only the value the type is hashed on?

I have a struct that has, among other data, a unique id:

struct Foo {
    id: u32,
    other_data: u32,
}

I want to use the id as the key and keep it inside of the struct:

use std::collections::HashSet;
use std::hash::{Hash, Hasher};
impl PartialEq for Foo {
    fn eq(&self, other: &Foo) -> bool {
        self.id == other.id
    }
}
impl Eq for Foo {}
impl Hash for Foo {
    fn hash<H: Hasher>(&self, state: &mut H) {
        self.id.hash(state);
    }
}

This works:

pub fn bar() {
    let mut baz: HashSet<Foo> = HashSet::new();
    baz.insert(Foo {
        id: 1,
        other_data: 2,
    });
    let other_data = baz.get(&Foo {
        id: 1,
        other_data: 0,
    }).unwrap()
        .other_data;
    println!("other_data: {}", other_data);
}

Is there any way to write baz.get(1).unwrap().other_data; instead of baz.get(&Foo { id: 1, other_data: 0 }).unwrap().other_data;?

An alternative might be a HashMap where the key is contained inside the struct. However, I can't have the id inside the struct and a duplicate id used for the key.