The following are from amongst the evidences that they have brought to support Istihsaan as a Hujjah (legal source of proof/evidence):

From the Qur’aan:

The Qawl of Allah Ta’Aalaa:

And His Qawl Subhaanahu:

In respect to the first Aayah the angle that they have used for proof is that it contains praise and commendation for the one who follows the best speech. The angle of the second Aayah is His Ta’Aalaa’s command to follow the best of what He revealed. If Istihsaan is not a Hujjah (proof) then why does this praise, commendation and matter exist.

As for the Ijmaa’:

Then this is represented in the Ijmaa’ of all of the Fuqahaa in respect to the permissibility to enter the bathroom without specification of the amount of time to be spent in it, the quantity of water used and without specifying the amount that has been paid... This is whilst it is contrary to the conditions and pillars of the ‘Aqd (contract) in Islaam.

Similarly, there is the Ijmaa’ of the Fuqahaa upon the permission to drink water from the hands of those who provide it without specifying the amount of water.

Those who held the view of Istihsaan attempted to clarify its meaning, specify its features and explain that it does not represent a statement or opinion based on desires and whims but rather it only represents the departure of one Qiyaas to another Qiyaas, or an exemption from a Qaa’idah Kulliyah (comprehensive principle), or the specification from a general Asl (origin) due to a Daleel that requires that departure or the exemption or specification.