Yes, if the resume is attached, readers can see all that details there.
However, a letter that is overly general and vague might generate so little interest that the reader might not even care to turn to the resume.
It should be sent in addition to a resume, and include meaningful credentials and show off your writing skills.
Though it may seem hard to fit all of this into 1 page, it’s easy to do as long as you follow a few simple steps!
Does your letter present plenty of specific detail but without making the letter too densely detailed?
Do you present hard factual detail (numbers, dates, proper names) that make you stand out as an individual?
(And certainly, please don't think of these as the "right" or the "only" things to put in the introduction to an application letter.) In the main parts of the application letter, you present your work experience, education, training whatever makes that connection between you and the job you are seeking.
Remember that this is the most important job you have to do in this letter to enable the reader see the match between your qualifications and the requirements for the job.
Are there comfortable 1-inch to 1.5-inch margins all the way around the letter?
Is there adequate spacing between paragraph and between the components of the letter? Does it avoid sounding overly aggressive, brash, over-confident (unless that is really the tone you want)?