MTG Salvation

Say my opponent has Wheel of Sun and Moon in play enchanting me, and I cast Gyruda, Doom of Depths.

As I put the top 4 cards of my library into my graveyard, Wheel's replacement effect puts them at the bottom of my library. Then Gyruda allows me to put one of these into play. Am I allowed to do so?

Gyruda doesn't specify that the card has to come from my graveyard, which suggests that even if the card has changed zone, this part of the ability wouldn't fizzle. Gatherer covers the case where the card has been exiled (for exemple if Rest in Peace is in play) and allows it:

If a replacement effect causes a player to exile the top four cards of their library instead of putting them into their graveyard as Gyruda’s triggered ability resolves, the creature card you choose may be one of those cards in exile.

Thanks for your help.

No. The differecne between exile and library is public zone vs. hidden zone. For public zones, rule 400.7 has an exception in rule 400.7h, which allows the effect to track the cards into exile. No such exception exists for hidden zones. So, the effect of Gyruda's trigger loses track of the cards, and cannot put any of them onto the battlefield.

400.7 An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are eight exceptions to this rule:
[...]
400.7h If an effect causes an object to move to a public zone, other parts of that effect can find that object. If the cost of a spell or ability causes an object to move to a public zone, that spell or ability’s effects can find that object.

Thanks for a very clear answer.