The takbeer for starting the prayer may count for the takbeer for bowing too

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Check below answers in case you are looking for other related questions:
Can one who has done tayammum lead in prayer people who have done wudoo’?
He is not sure whether he said the opening takbeer or not

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Related Answers:
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Can one who has done tayammum lead in prayer people who have done wudoo’?
He is not sure whether he said the opening takbeer or not

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