Constraint on row value based on values in other rows

Is it possible to have a table with four columns:

CREATE TABLE accrual (
    add_date date NOT NULL,
    user_id integer NOT NULL,
    rate integer NOT NULL,
    amount numeric(7,3)
); 

and then constrain it so that if I already have one entry like

('2016-04-01', 3, 120, 25.6)

an attempt to insert another entry with the same date and user_id but a different rate would fail? i.e.

('2016-04-01', 3, 140, 15)

would fail, but

('2016-04-02', 3, 140, 15)

or

('2016-04-01', 4, 140, 15)

or

('2016-04-01', 3, 120, 15)

would be fine?

To be clear, the date and user_id are basically like an index, except duplicate indices are totally fine as long as the rates are the same. The amount is not constrained.

I am working with a postrgesql 9.5 database, and I am using PHP. My guess is that the easiest thing to do is to write some PHP code to perform the check. The closest question I could find to this was this one:

trigger or check constraint insert values based upon existence of others

but it is about an Oracle database and is slightly different.

Thanks for any suggestions!!!