What is the evidence that the wife's consent is not a prerequisite for a second marriage, and that it is permissible to conceal the second marriage from her, and is the condition "if her husband marries, she has the right to divorce" still valid?

The fundamental principle is that whoever stipulates informing the first wife when marrying another is the one required to provide proof, and the default is no stipulation. It has not been reported that the Prophet, peace and blessings be upon him, or his companions sought permission from their wives, and this is sufficient in establishing the ruling. The Permanent Committee for Issuing Fatwas responded that pleasing the first wife is not an obligation, but rather a noble moral quality. Sheikh Ibn Uthaymeen issued a fatwa that informing the wife is neither a condition nor an obligation, and there is no harm in concealing it if the husband fears her disapproval or harm to his household, especially since society's rejection of this legal ruling might prompt the husband to conceal it.