I have added the necessary qualification.  Regarding the original lead, it was a mess. Amongst other things the original lead had redundancies, it employed terms without first defining them or linking to a definition, sometimes the term "compound" was used and other times "statment" was used, the relatively minor matter of material implication vs. logical entailment was too long, used an awful example and just confused what preceded it.  In the lead it would have been sufficient to just say something like: "The material conditional is to be distinguished from logical entailment (which is usually symbolosed using [double turnstile]."  The distinction can then be detailed in the body of the article.  Also the failure to even mention propositional calculus  which is the context in which someone is most likely to look up the meaning of the operator  was an unacceptable omission.  By the time someone reaches the study of paraconsistent logical systems they will likely have no need to look up what a material conditional is on Wikipedia.  A novice is most likely to look up this entry in wikipedia and they will most likely have encountered the operator in the context of classical/Boolean propositional calculus.