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If Vengeful Pharaoh is no longer in your graveyard when the triggered ability would resolve, the triggered ability won't do anything.

If multiple creatures deal combat damage to you and to a planeswalker you control simultaneously, Vengeful Pharaoh will trigger twice. The first trigger will cause Vengeful Pharaoh to be put on top of your library. The second trigger will then do nothing, as Vengeful Pharaoh is no longer in your graveyard when it tries to resolve. Note that the second trigger will do nothing even if Vengeful Pharaoh is put back into your graveyard before it tries to resolve, as it's a different Vengeful Pharaoh than the one that was there before.

If multiple creatures deal combat damage to you simultaneously, Vengeful Pharaoh will only trigger once.

If the attacking creature is an illegal target when the triggered ability tries to resolve, it won't resolve and none of its effects will happen. Vengeful Pharaoh will remain in your graveyard.

If your own attacking creatures deal combat damage to you or a planeswalker you control (perhaps because combat damage was redirected), Vengeful Pharaoh will still trigger. You must target and destroy one of your own attacking creatures.

Vengeful Pharaoh must be in your graveyard when combat damage is dealt to you or a planeswalker you control in order for its ability to trigger. That is, it can't die and trigger from your graveyard during the same combat damage step.