Drinking water instead of gargling the mouth when making ghusal

I performed fard ghusl. I performed the two fard of washing my whole body and putting water in my nose but before I rinsed my mouth, I drank a glass of water (to fulfill the obligation of gargling, as I was advised to drink a glass of water to fulfill the gargling) but then I forgot about rinsing my mouth. I rinsed my mouth the next day when I remembered but did not gargle as I had already drank water the day before it to suffice for gargling. So is the fard of washing the mouth now complete and my ghusl valid?