Mew is known as a mirage, as it is very rarely seen by people. It's one of the rarest Pokémon that exist, in fact, and it's believed to be one of the ancestors of all Pokémon.

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In its Mega Evolution, this becomes readily apparent. The link to the other ancestor, Arceus, is strengthened and it returns Mew to its full power after ages. Because of this, it gets the ability Omnigene, which is known as one of the most powerful abilities that exist.

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In battle, Mega Mew is one of the most powerful Pokémon to ever appear. It can learn every single move in existence, including moves like Roar of Time and Judgement. Not only that, but it can still hold an item, as it can Mega Evolve after learning the move Mirage Call, which acts similar to Metronome but only uses the signature moves of other Legendary Pokémon.

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And as said previously, it has one of the most powerful abilities that exist. Omnigene. This ability acts like Protean in that it changes the user's type to the move it uses. Additionally, it boosts Same Type Attack Bonus like Adaptability. To top it all off, the user's type on the first turn can be determined by holding one of Arceus's Plates.

The only ability known to even compare to Omnigene in power is Wonder Guard, it is THAT powerful. Because of this, only Mega Mew and a certain other Pokémon have this deific ability.