Alpha invariants of birationally bi-rigid Fano 3-folds I

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold K"{a}hler-Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.