.........................First of all, remember, all the founders of the Dharmic religions(Buddhism,Sikhism, Jainism) were born Hindus i.e they all originated from this ONE Vedic Religion(Hinduism)....which again implies that there was ONLY ONE religion in Ancient India.
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Now, the fact that, India has always been Invaded(so other religions came into India) BUT Indians(Hindu Kings) never Invaded other countries(so Hinduism, never got a chance to spread outside the subcontinent at that time) implies that this religion can be attributed to a very specific set/group of people living ONLY in the subcontinent.
So, the bottomline is.....that the ONLY religion existed in Ancient India was Hinduism, It is a very well-defined religion and it can be attributed to a very specific group of people living ONLY in the subcontinent.
Therefore, India(ancient/modern) and Hinduism cannot be separated.
Ancient Indians=Hindus and viceversa.
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