Valmiki Ramayana Aranya Kanda Sarga 37 Shloka 10
Original Shlokaवञ्चितं पितरं दृष्ट्वा कैकेय्या सत्यवादिनम्। करिष्यामीति धर्मात्मा तात प्रव्रजितो वनम्।।3.37.10।।
1 source checked for this shloka
तात dear, सत्यवादिनम् always speaks the truth, पितरम् father, कैकेय्या by Kaikeyi, वञ्चितम् deceived, दृष्ट्वा after seeing, धर्मात्मा righteous man, करिष्यामि इति saying I will do it, वनम् forest, प्रव्रजितः came.
O dear, seeing that his truthful father was going to be deceived by Kaikeyi, righteous Rama himself offered to fulfil the promise of his father and came away to the forest.