What does vanas mean in Spanish?

What's the meaning of the Spanish word vanas? Here's a list of translations and example phrases.

English Translations
Phrases in Context
Las protestas de Filipo, fundamentadas en que no había violado ninguna de las condiciones de la paz de Fénice, fueron vanas y comenzó la guerra.
Philip's protests, grounded in that he had not violated any of the conditions of the peace of Fenice, were vain and the war began.
Patru, el mismo que disuadió a La Fontaine de escribir sus Fábulas y a Boileau de componer su Arte poético, cansado de estas discusiones vanas, fue expulsado de la Academia.
Patru, who dissuaded La Fontaine from writing his Fables and Boileau to compose his poetic Art, tired of these vain arguments, was expelled from the Academy.
No sólo por no parecer una persona que haya proferido palabras vanas, tanto más que ya he hablado anteriormente, sino porque estoy seguro de que ello reportará ciertos beneficios al objeto de nuestros estudios.
Not only because I do not look like a person who has uttered vain words, all the more so as I have already spoken, but because I am sure that this will bring certain benefits to the object of our studies.
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