The matter being of great moment, and Jonathan doubting the truth of it, David confirms his word with an oath, which follows in the end of the verse; only he interposeth a reason why Saul concealed it from Jonathan.
Related Commentaries of 1 Samuel 20:3
1 Samuel 20:3
3 And David sware moreover, and said, Thy father certainly knoweth that I have found grace in thine eyes; and he saith, Let not Jonathan know this, lest he be grieved: but truly as the LORD liveth, and as thy soul liveth, there is but a step between me and death.