It's seemingly not our withdrawing that would cause Iran to pull out also, but our threat to resume sanctions. And, reportedly, China and Russia would for sure block that in the UN, leaving us only our relatively minor unilateral ones. Most or all NATO nations wouldn't support reimposing their own sanctions either.
Despite Iran's threats, they and the others members might decide to continue it without us, Trump having abandoned any leverage we have now, though he and Bolton probably imagine The Bomb as their leverage. Iran wants to continue the deal, of course.
It seems the biggest threat isn't Iran itself but a rift in NATO, which would be an enormous gift to Putin, of course, and threat to the planet.
President Rohani: I have spoken with Macron several times by phone, and one time in person at length. I have told him explicitly that we will not add anything to the deal or remove anything from it, even one sentence. The nuclear deal is the nuclear deal, he said during a conference in the northwestern city of Tabriz. He suggested Macron has no right to amend an agreement signed by seven nations.
As long as our interests are guaranteed we will remain in the deal, whether the U.S. remains or not, Rohani said. But he added that if our benefits are not guaranteed, we will not remain in the deal, no matter what the circumstances are.
https://www.haaretz.com/middle-east-news/iran/.premium-what-happens-if-trump-pulls-out-of-the-iran-nuclear-deal-1.6031700