The Gita is no more than a lengthy, inspirational passage, excerpted from a larger, epic poem. It was never intended to be proof, evidence, or anything -- except a discussion of metaphysics and dharma. It's not even considered shruti.
It looks like you did not see the double quotes -- and the whole sentence
Let me explain if it is not clear.
I said "The proof is in Bhagavad GeetA - it is "proof" for me just as <replace scripture/religion here> is "proof" for you."
What does this mean?
If a person says "<their scripture/religion> is proof" [to them]
Then I can say "to me Bhagavad Geeta is proof"
and you may ask "of what?"
For one, the yoga explained in the Geeta work!
Karma Bhakti sAnkhya Jnana Dhyana Raja yoga - they all work!
Where is the proof that they work?
You are the proof! The sAdhak. The yogi who sees progress in themselves is the proof to themselves.
As for not being shruti, it is the cream of all the milk obtained by milking the Upanishads that ask you to test it out and see for yourself -- and Upanishads are shruti.
sarvopanishado gAvo dogdhA gopAla nandana |
pArtho vatsa sudhirbhoktA dugdham geetAmrutam mahat ||
-- GeetA Mahatmya
Meaning: All Upanishads are cows,
and Shri KRshNa , son of the cowherd Nanda, is the milkman who milks the cows (Upanishads)
OR
The cowherd KRshNa Gopala, who is ever blissfull (nandana - AnandI), is the milkman.
Arjun is the calf, who drinks this immortal nectar of milk called the Bhagavad GeetA.