Vanish into thin air

Is it possible that the phrase 'to vanish into thin air' actually comes from Orpheus and Eurydice by Virgil? When Eurydice vanishes, it is written: ...and suddenly fled, like smoke vanishing in thin air.

Probably people who use it in English are directly referencing Shakespeare: at the end of As You Like It, Prospero says "These our actors,
As I foretold you, were all spirits, and Are melted into air, into thin air". However, Shakespeare had a grammar-school education which would certainly have included screeds of Virgil, so there's every possibility that he remembered and used Virgil's simile. (VSD)