On 23 June 1596, an Ottoman Army marched from the city of Istanbul. Commanded by Sultan Mehmed III, the army marched through Edirne, Filibe , Sofia and Niš to arrive at Belgrade on 9 August. On 20 August, the army crossed the River Sava by bridge and entered the Austrian territory of Siren. A war council was called at Slankamen Castle, and it was decided that they would begin a siege on the Hungarian fort of Eger . The fort controlled the communication routes between Habsburg Austria and Transylvania, all of whom were in revolt against the Ottoman suzerainty. However, news soon arrived that the Austrians had besieged and succeeded in taking over the Castle of Hatvan and had killed all the Ottomans housed there, including the women and children. The Ottoman Army started a siege on the fort of Eger on 21 September 1596, and by 12 October the castle had capitulated. As a retaliation to the Hatvan castle massacre, the defenders of this castle were all executed. Not long after, Ottoman command received the report that a mixed army of Austrians and Transylvanians were advancing towards the Ottoman expeditionary force. A war council was conducted under Grand Vizier Damat Ibrahim Pasha. It was decided that the Ottoman Army should march out of the Erlau castle so as to meet the Austrians at a suitable battle terrain. The Sultan thought that the Ottoman army should disengage and return to Istanbul; it was with great difficulty that he was persuaded to engage the enemy forces. The most realistic troop strength figures seem to be 40,000-50,000 for the Christian and 80,000-100,000 for the Muslim army. The Christian army had 10,000 Austrians, 4,000 Germans, 3,000 reiters, 13,000 Hungarian light cavalry and 10,000 Transylvanians, for a total of 40,000 men.
Question: How many more Christian troops were Hungarian and Austrians than Germans and reiters and Transylvanian?
Answer: 6000