It is proven that the Sahabah used yeast
It is proven that the Sahabah (may Allah be pleased with them) used yeast in their bread, as al-Bukhari (5432) narrated that Abu Hurayrah said: I used to keep company with the Messenger of Allah (blessings and peace of Allah be upon him) for I was content with just a little to eat, and at that time I did not eat leavened bread, or wear silk…
Al-`Ayni said in As-Sihah, 2/650: Leavened bread is bread that is made with yeast. End quote.
The effect of yeast on food and the ruling thereon
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: What is the ruling on the yeast that they use in flour to help ferment it and make it easy to cook it, because some people say that it cause intoxication and it is not permissible to use it?
He (may Allah have mercy on him) replied: My response is that is that there is nothing wrong with putting yeast in the dough to make it ferment and rise, because that does not affect it at all.
Moreover, I do not think that this yeast would cause intoxication if a person were to consume a large amount of it.
In principle, all foods, all drinks and all clothing are permissible unless there is evidence to indicate that a thing is prohibited, because Allah, may He be Exalted, says: {It is He Who has created for you all things that are on earth; furthermore He turned to the creation of heaven, and made seven heavens. And He has knowledge of all things} [Al-Baqarah 2:29].
So there is nothing wrong with adding yeast to the dough to make it rise.
End quote from Fatawa Nur `ala ad-Darb, 20/2.
Therefore, if it is proven that fermentation only happens after the stage where the yeast turns into alcohol, this is proof for those who say that there is nothing wrong with using alcohol or yeast to produce something permissible, so long as the purpose is not to have alcohol in it. This is the view of ash-Shafa`i.
Ibn al-`Attar (may Allah have mercy on him) said: Rather it is prohibited if the grapes are pressed for the purpose of making wine. But if they are pressed for the purpose of making vinegar, then it is prohibited whilst they are in an alcoholic state but when they are being pressed, they are not prohibited because they do not cause intoxication, and the aim of pressing them is not to make alcohol. And when they become vinegar, the aim of pressing them is not to make alcohol. The Prophet (blessings and peace of Allah be upon him) said: “What a good condiment vinegar is,” and if it was prohibited, he would not have said that, because it cannot be imagined that you can get vinegar except after it was alcohol.
End quote from Al-‘Uddah fi Sharh al-‘Umdah, 3/1647.
As for yeast, no matter what state it is in, it does not remain in the bread that is eaten; rather it transforms and is absorbed when it is baked.
Shaykh Zakariya al-Ansari (may Allah have mercy on him) said: … or he says, “If I eat food you have cooked, you are divorced,” then she puts the pot on the fireplace without lighting the fire under it, and someone else lights the fire, or he says: “If I eat your food, then you are divorced,” then he adds yeast from her food to his dough, meaning that he takes some yeast or water or salt and mixes it with flour and makes dough, and eats what he cooked or made dough with – he has not broken his oath. That is because the one who cooked the food in the first instance is someone other than the wife, and in the second instance her food was absorbed into something else. So it is similar to the case if he were to swear that he would not eat ghee, then ate it in `asidah [a gruel made with flour and ghee] into which it was absorbed… (3/329).
It says in Al-Muhit al-Burhani (3/491) – a Hanafi book –: He swore that his wife would be divorced if he ate his brother’s food, then his brother put yeast in the flour of the one who had sworn the oath, and he baked it and ate it.
Al-Hasan ibn Ziyad (may Allah have mercy on him) said: He does not have to divorce his wife, because the yeast is gone. End quote.
Therefore so long as the bread would definitely not cause intoxication if a large amount of it was consumed, and the alcohol that could be present during fermentation is a small amount and it evaporated with the heat when it was baked, there is nothing wrong with eating the bread.
It is not like one who bought wine or alcohol and put it in the food, or he bought some wine and turned it into vinegar. Rather in this case he bought something permissible that does not cause intoxication, namely yeast, and put it in the dough, so if some alcohol resulted from that when the bread fermented, then the traces of alcohol disappeared, there is nothing wrong with that.
And Allah knows best.