Dropping the a of la is not slang and it’s actually the 16th rule of the fundamento:
- The a of the article, and final o of substantives, may be sometimes dropped euphoniae gratia, e.g. de l’ mond'o for de la mond'o; Ŝiller’ for Ŝiller'o; in such cases an apostrophe should be substituted for the discarded vowel.
However it’s not very common in speech and it’s mostly used in poetry or lyrics. For example it can be found several times in La Espero which was written by Zamenhof:
Sub la sankta signo de l' espero
kolektiĝas pacaj batalantoj,
kaj rapide kreskas la afero
per laboro de la esperantoj.
It also appears in the title of the Esperanto translation of one of the books of Tintin: La Templo de l’ Suno.
According to PMEG, it is usually only used after a preposition that ends in a vowel and then the l is pronounced as if it was part of the previous word. So in these examples the de l’ is pronounced del. Note however that the l’ is always written as a separate word.