You can use Normal
, documentation says it deal with special forms but ConditionalExpression
is not explicitly mentioned there but documentation says it deals with special forms.
p1 = y /. {First[Solve[x^2 + y^2 + x == 1, y, Reals]]} // First
ConditionalExpression[-Sqrt[1 - x - x^2], 1/2 (-1 - Sqrt[5]) < x < 1/2 (-1 + Sqrt[5])]
Normal @ p1
-Sqrt[1 - x - x^2]