The son born of the Shudra wife should not be considered as invested with the dignity of a Brahmana on account of his being unskilled (in the scriptures and the duties ordained for the Brahmana). Only those children who are born of wives belonging to the three higher castes should be considered as invested with the dignity of Brahmanas.
अब्राह्मणं तु मन्यन्ते शूद्रापुत्रमनैपुणात्। त्रिषु वर्णेषु जातो हि ब्राह्मणाद् ब्राह्मणो भवेत्॥