Valmiki Ramayana Ayodhya Kanda Sarga 37 Shloka 24
Original Shlokaआत्मा हि दारास्सर्वेषां दारसङ्ग्रहवर्तिनाम्। आत्मेयमिति रामस्य पालयिष्यति मेदिनीम्।।2.37.24।।
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दारसङ्ग्रहवर्तिनाम् of men who guard their wives, सर्वेषाम् for all, दाराः wife, आत्मा हि is the very soul, इयम् this Sita, रामस्य Rama's, आत्मा इति soul, मेदिनीम् this earth, पालयिष्यति will rule.
For every householder, his wife is the soul. Since Sita is the soul of Rama, she can rule this earth.