Tub trap height question

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Hello all - happy 4th.

I have a question about a combined tub/shower trap that I haven't seen covered here after some searching. I'm installing a tub/shower combo in a 2nd floor guest bath (pretty basic 60" tub, haven't picked one yet). It's an old house with 2x6 joists, but the room below has a lowered ceiling so I have over 1' of height to work with. Structurally the room is fine - the joist span is only 7' and they are spaced 12" on center with no notches or cuts.

The drain will run under the tub parallel to the joists, and I will vent it properly. However the bearing wall supporting the joists is offset about 5" into the bathroom from the bathroom wall itself - if I understand the tub/shower rough-in correctly that is directly below where the trap for the shower will be so I only have 5.75" (not 5.5") of height there.
HTML:
          |  |
    Tub   |  |
  ____________
      JOIST
  _____________
       |  |
       |  |

Is that going the be enough height to run a 2" trap assuming the tub is sitting on the floor? How about 1.5" (I'd rather use 2" if possible) If not, is there any way to offset the trap 3-4"?

Hope that made sense, and thanks in advance for any help
 
tub trap

A tub/shower only needs 1.5"trap,it is common practice to use 2"p-trap for shower only,although the IPC requires minimum 1.5" trap
 
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