But it still won't tell if it is wrong, if the wrong temp is inserted in both EFB & FMC.
that is not what we are discussing though Rat. What happened here is that the EFB temperature was entered correctly, the correct assumed temp was entered into the FMC , but the N1 was wrong. So in this case, simply checking the N1 from the EFB is the same as the N1 in the FMC does in fact trap the error.