Forum:Aegis+Levia+Ocean question

The is a scenario in which these cards are in play:

-Levia Dragon-Daedalus

-A Legendary Ocean

-One or more Level 4 WATER Monsters (i.e.: "Gagagigo")

-[set face-down] Aegis of the Ocean Lord

1) "A Legendary Ocean" causes my Level 4 Monster, "Gagagigo", to downgrade to Level 3, allowing them to be protected by "Aegis of the Ocean Lord", which I activate during my Main Phase.

2) I then activate "Levia Dragon-Daedalus'" effect, sending "A Legendary Ocean" from the field to the Graveyard to destroy all cards on the field except itself.

Now comes the question:

---Since "Aegis of the Ocean Lord" only protects WATER Monsters Lv3 and lower, and "A Legendary Ocean" is the only thing that allows "Gagagigo" to meet that requirement, would activating "Levia Dragon's" effect and sending "A Legendary Ocean" to the Graveyard as the activation cost, in turn, cause "Gagagigo" to become Lv4, losing its "Aegis" protection from "Levia Dragon's" effect, and end up being destroyed?