As José answered more gracefully, you don't need to learn the syntax but you do need to learn the semantics, the performance gotchas, and for most projects I'd say you'll probably need to consume Erlang documentation which is certainly a learned skill.
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You def dont need to learn Erlang to code in Elixir (other than maybe the very basics to interact with some Erlang libraries like ETS).
As José answered more gracefully, you don't need to learn the syntax but you do need to learn the semantics, the performance gotchas, and for most projects I'd say you'll probably need to consume Erlang documentation which is certainly a learned skill.