YAH!!! Maybe there is no escaping the law
No.
Pretty much sure you'll have been bitten by a water snake.
Or whatever.

+

You done with the kid yet? I had to get some ventilation.
Do you think he'll go for the top bunk or the bottom bunk? It's a very important question.
And my new choice of leg or midriff covering doesn't hide much.
Besides, piano kind of sucks. It's got too many keys. And not enough pedals. Good Wulitzer EP by JPJ there, or just a Rhodes through a tremolo effect. I think JPJ is just holding down the bass with one of those Moog devices: sounds like it, anyway. I think an elephant on quaaludes could hold that down while still doing the EP stuff. And I'm not that great at using heel-toe for an actual bass line. But vamping on I-perfect Fifth or perfect fourth is something I think even a mere piano player could do.
There's a brief gliss behind about midway through Page's solo that makes me think Rhodes, but JPJ could have easily had both set up, with the infamous "patch to the front" on the sawed-off Wurlitzer on top of the Hammond. (64 key manual from A-->C, and the aux output is on the bottom of the keyboard, which you can patch or have patched to the front of the KB and get rid of those dinky little spindly legs and put it on top of the Hammond, typically.
But, I would have just taken the Rhodes and done it like that. (E-->C, 73 keys on the stage model). The common denominator is, of course, the high C note, just like on a Hammond organ manual. At a right angle to the organ or the acoustic piano.