Welding1 is correct. Qw-424.1 is very clear. If you have a WPS that has been qualified using P4 to P4 you can use the procedure to weld P4 to P4, P4 to P3, and P4 to P1 materials. I would write another WPS for the welding of P4 to P1 and support this WPS with the PQR for the P4 to P4 material. The catch here is that all other essential variables must remain the same. For example, you can not change the filler metal.
ASME Section IX interpretation IX-89-58 deals with this subject.
Question (1): “A WPS is qualified for P5 to P5 base metals. Will the PQR for this procedure also support a new WPS for P5 to P4 base metals if all other welding variables remain the same?
Reply (1): “YES”
Although the P numbers are different, the concept is the same. I would however caution you as to your application. I do not know what code you are fabricating to (section I, B31.1). In ASME Section I the PWHT for P4 is 1100 F this also happens to be the PWHT for P1 material (no problem here). However, in ASME B31.1, the PWHT for P4 material is 1300 to 1375 F. Since the lower critical temperature for P1 material is ~1340 F I would be very hesitant to use the procedure to weld P4 to P1. If your current WPS shows a PWHT temperature in this range, I would suggest you qualify another WPS using P4 to P1 material.
You have to keep in mind that the ASME codes are primarily safety codes and not necessarily operational codes. The do not consider all of the different metallurgical combinations that may be possible for fabrication. It is up to the user of the code to make sure that the materials they are welding are metallurgically compatible with respect to PWHT, weld design, service requirements, and mechanical properties.
Hope this helps.