Why is classic if writing and inline if writing are not behaving the same way?

I got this code

firstId = True
       
for x in [1,2,3,4,5]:
    firstId = False if firstId else print(str(x)+ " " + str(firstId))
    
print ("What is happening here ???")

firstId = True
       
for x in [1,2,3,4,5]:
    if firstId: 
        firstId = False
    else:
        print(str(x)+ " " + str(firstId))

And strangly i have this output

2 False
3 None
4 None
5 None
What is happening here ???
2 False
3 False
4 False
5 False

From my understanding both if statement should behave the same way.But the boolean is not. I can't understand why the boolean somehow becomes None. Can someone explain what is happening?