PokéBase - Pokémon Q&A
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Yes.
Mew can learn every TM.

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It's kinda funny that it can learn attract though.
Why is that funny? Mew is pretty kawaii...
Attract doesn't do anything since Mew is genderless.
The only other genderless Pokemon that can learn attract is Cryogonal and it still fails. :P
Rare scene right there.