Yes, Extremely strong - it's among the extremely few statements which are uncontroversial in nutrition.
google scholar -> vegetables health -->
http://ajcn.nutrition.org/content/70/3/475s.full
--> assorted references
Edit: I think it's more accurate to say that vegetable deprivation is extremely harmful. It's not like eating additional vegetables leads to additional health!
Psychologically speaking, it is helpful to think of eating vegetables as the default state which we actively deviate from, not a thing which we actively do to stay healthy. That's why I like words such as "sedentism" - it makes you feel like you are actively harming your body rather than passively allowing it to be harmed, similar to "alcoholism".
Some very basic questions given my complete dearth of knowledge:
What are micro-nutrients and anti-oxidants? Why are they good?
What is the minimum quantity of vegetables a normal adult would need to get the benefits described? Do they scale at all with increased consumption?
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous "stupid" questions thread is at almost 500 questions in about a month, so I think it's time for a new one.
Also, I have a new "stupid" question.