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Assuming upanishads can be considered as part of vedas -

A similar verse is found in Katha upanishad 2.1.10 second half

mṛtyoḥ sa mṛtyumāpnoti ya iha nāneva paśyati ||

(Translating and interpreting according to advaita.)

He who sees multiplicity here, goes from death to death.

Explaining this Sankaracharya says -

This being so, he who here deluded by ignorance, which consists in seeing difference by the nature of the conditions sees in the Brahman which is one, a variety, thinking thus ‘I am other than the highest Brahman and the highest Brahman is other than I’, goes from death to death, i.e., is again born and dies; so, one should not see thus.

The meaning is that a person who does not know brahman, keeps taking birth and dying again and again.