You could say that the rain is antecedent to the grass getting wet. The Oxford English Dictionary writes that:
A thing or circumstance which goes before or precedes in time or order; often also implying causal relation with its consequent.
So, antecedent is often paired with consequent. They write further that in logic:
Hence, in various special applications, of which the logical and grammatical are the earliest uses of the word in English: Logic. (Opposed to consequent.) The statement upon which any consequence logically depends; hence †(a) The premisses of a syllogism (obs.); (b) The part of a conditional proposition on which the other depends. †(c) By some early logicians the subject and predicate were called antecedent and consequent.
For example, a usage in writing is:
1870 F. C. Bowen Logic v. 128 All Hypothetical Judgments obviously consist of two parts, the first of which is called the Condition or Antecedent.