Verse 3

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आत्मानात्मप्रतीतिः प्रथममभिहिता सत्यमिथ्यात्वयोगा -द्द्वेधा ब्रह्मप्रतीतिर्निगमनिगदिता स्वानुभूत्योपपत्त्या ।आद्या देहानुबन्धाद्भवति तदपरा सा च सर्वात्मकत्वा -दादौ ब्रह्माहमस्मीत्यनुभव उदिते खल्विदं ब्रह्म पश्चात् ॥ ३ ॥

In plain words

First comes the discernment of real Ātma—the Self—from unreal Anātma, the non-self. Then the Vedas unfold a twofold realization of Brahman, confirmed in direct experience: first ‘I am Brahman’ dawns while one is still connected with the body; afterwards the whole universe is known as Brahman, the Self of all.

Close to the Sanskrit

First, cognition of Ātma—the Self—and Anātma, the non-self, is declared through their connection with the real and the unreal. The realization of Brahman, declared twofold by the Vedas and established through one's own experience, first arises in connection with the body and then through being the Self of all. At first the experience ‘I am Brahman’ dawns; afterwards, ‘all this indeed is Brahman.’