Praise be to Allah.
Yes, this method is sufficient. The scholars unanimously agreed that what is obligatory in Wudu is to wash each part once, although washing each part two or three times is Sunnah.
Al-Bukhari (157) from Ibn `Abbas (may Allah be pleased with him) who said: The Prophet (peace and blessings of Allah be upon him) did Wudu washing each part once.
An-Nawawi (may Allah have mercy on him) said: “The Muslims unanimously agreed that what is obligatory is to wash each part once, and that washing each part three times is Sunnah. There are authentic Hadiths which mention washing each part once, and each part three times, and washing some parts three times, some two times and some once.
The scholars said: the difference indicates that all of these are permissible, and that washing each part three times is most perfect and washing each part once is sufficient. This is how the variations in the Hadiths are to be interpreted.”
Ash-Shawkani (may Allah have mercy on him) said: “The authentic Hadiths speak of washing each part once, twice or three times, or washing some parts three times and some twice. The differences indicate that all of these are permissible, and that washing three times is most perfect and washing once is sufficient.” (Nayl Al-Awtar, 1/188)
But we should not persist in washing each part only once and not do that which is more perfect, because by doing so we are depriving ourselves of more reward.
For more details, please refer to the following answers: 69761 , 45535 , 200648 , and 85065 .
And Allah knows best.
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