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Existential Introduction:
Now if we have any sentence as, A, and variable, v, that does not occur in A, so then for any ground term, g, such occurs in A, than we can turn A into an existentially quantified sentence by substituting v for g as:
∃A /v Subst({g/v}, A)
So now we have for example like, if we know likes(jerry, ice_cream), so then we can infer that ?X (likes(X, ice_cream)), just because the constant jerry doesn't appear anywhere else in the original sentence. Thus the conditions v and g don't occur in A is for similar reasons as those given for the before this rule. Now as an exercise, here find a situation when ignoring this condition would mean the inferred sentence did not follow logically from the premise sentence.
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