Gimbal Lock with Quaternion.AngleAxis?

I have no idea why despite changing eulerAngles to Quaternion.AngleAxis, my camera still snaps forward in world direction.

// inside Update() in my camera/mouse movement script
float mouseX = Input.GetAxis("Mouse X") * mouseSensitivity;
float mouseY = Input.GetAxis("Mouse Y") * mouseSensitivity;

xRotation -= mouseY;
yRotation += mouseX;

// Clamp the rotations locally
xRotation = Mathf.Clamp(xRotation, -90f, 90f);
yRotation = Mathf.Clamp(yRotation, -35f, 35f);

// Apply the local rotations
Quaternion.AngleAxis(xRotation, Vector3.right);
player.transform.rotation = Quaternion.AngleAxis(yRotation, Vector3.up);

I believe the very last line is the issue, but no idea why.