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で遊んじゃ

don't play with …

→ で
phrase Very common #1,874
don't play with … An informal contraction used in warnings, usually followed by ダメ or だめ. The particle で marks what someone is playing with.
JA: そのスマホで遊んじゃダメ。
EN: Don't play with that phone.

たき火で遊んじゃだめだよ。

Don't play with the campfire.

その鍵で遊んじゃダメ！

Don’t play with that key!

その鍵で遊んじゃダメよ。

Don't play with that key.