# SAT satisfaction with 10 variables

I am trying to prove that the next problem is NPC:

$$A=$${$$<\phi>|\phi \,\,\,is\,\,\,a\,\,\,CNF\,\,\,and\,\,\,has\,\,\,satisfying\,\,\,assignment\,\,\,where\,\,\,exactly\,\,\,10\,\,\,variables\,\,\,are\,\,\,TRUE$$}

I am trying to find polynomial mapping reduction from SAT but I can’t find a way to force exactly 10 variables to get TRUE assignment. My idea was to create new formula, with 10 clauses, each clause is the intersection of a new variable $$x_i$$ with the old formula, but I don’t see how my idea helpful.

I would appreciate help.