How to prove that Nirvana term in Gita isn’t borrowed from Buddhism?
Totally false claim. Adding Nirvana makes no sense later because the the concept was already present in in Mahabharata before that.
'Nirvana' is one of the names of Vishnu in Vishnu sahasranama of Mahabhrata, Here is excerpt from BORI CE translation-
Note that I have highlighted the term 'Nirvana'. I referred to other Sanskrit cource the name mentioned is निर्वाणम् which means 'All-Bliss'. Its highly unlikely that people took a Buddhist name and made it one of the names of lord Vishnu.
Acharya's who opposed the Buddhist philosophy, in their commentaries of Vishnu-Sahasranama never objected on this particular name.
Before this also in Anusashan Parva the term 'Nirvana' occurs twice the reference are as follows-
The learned ones have said that nirvana is supreme.Therefore, one should not act in accordance with what is pleasant and what is unpleasant. However, a person who follows kama does not attach importance to this. I act wherever I have been appointed. All the beings have been appointed by destiny.
Here is another reference from Mahabharata itself-
It is my view that nirvana is extremely difficult to attain. There are many obstacles along the path. Therefore, those who follow this dharma, are devoted to truth, generosity and austerities, have the quality of not causing injury, are devoid of desire and anger, are engaged in the task of protecting the subjects, are based on supreme self-control and fight for the sake of cattle and brahmanas, obtain the supreme
Also the term Mentioned in Bhagwat gita is same as the name in Vishnu Sashranama-
लभन्ते ब्रह्मनिर्वाणमृषय: क्षीणकल्मषा:| छिन्नद्वैधा यतात्मान: सर्वभूतहिते रता: || 5.25||
कामक्रोधवियुक्तानां यतीनां यतचेतसाम् | अभितो ब्रह्मनिर्वाणं वर्तते विदितात्मनाम् || 5.26||
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