Is a spent UTXO immediately deleted from the UTXO set?

Suppose A spends a UTXO of 5 BTC. The transaction is sent to the mempool. Will the 5 BTC UTXO be instantly deleted from the UTXO set? If no, can this UTXO still in the UTXO set be used to make another transaction? Can this UTXO be used while it is in the mempool (unconfirmed transaction)?



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