Hi Benoit. I made some changes to itexp as you suggested, I changed the 
conditions so it works with NN0 and I changed the name to itgexp as "itg" 
seems to be the common abbreviation for integral. I am very happy to change 
to either itgmon or itgpow, it's fine with me, however I think that it 
should definitely match dvexp <http://us.metamath.org/mpegif/dvexp.html>and 
maybe also the exp theorems in Glauco's Mathbox 
<http://us.metamath.org/mpegif/mmtheorems294.html>. So I think I am very 
happy to change and I think someone with more authority than me would need 
to make the change global and do I find replace in all theorems that rely 
on dvexp etc if this change is to happen.

I'm afraid at the moment I don't want to start on replacing everything with 
(ph ->, that sounds like quite a lot of tricky work, I might get to it in 
the future though. I can see that a lot of thought has gone into deduction 
vs inference etc. Is it good practice in general to write everything in 
deduction form ( I mean starting with "( ph ->" )?

To anyone, I am a little stuck with this next theorem, I have DJVars again 
at line 74 and I am not sure I am taking the right approach. I am happy to 
keep working away on it however it would be helpful if anyone was willing 
to advise whether I am taking the right approach or not, do I have the 
right sort of notation? Some theorems seem not to accept <. x , y >. in the 
place of an &S1 which means it is a bit challenging, but probably still 
doable. Here <https://pastebin.com/AEMbVULE>is the text, this is the 
theorem:

h1::subarea.1      |- A e. dom area
h2::subarea.2      |- C C_ RR
h3::subarea.3      |- B = { <. x , y >. | ( <. x , y >. e. A /\ x e. C ) }
!qed::             |- B e. dom area

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