I want to proof if L1 is equal to L2. I found a slide related to that. However, I can't understand two things, I have represented with (1) and (2) in the attached image

(1) Initially we started with (L1 intersection L2') U (L1' intersection L2) = phi but in the next step it was changed to:

(L1 intersection L2') and (L1' intersection L2) = phi , I can't understand this. We could have started with: (L1 intersection L2') and (L1' intersection L2) = phi

(2) In (2) L1 intersection L2' was removed with circles showing L1 subset of L2 and after the circles we have L2' and similarly in the next part of that line we have: L1' intersection L2 was removed with circles showing L2 subset of L1 and after the circles we have L1'.

Somebody please explain me the (1) & (2) points?

I dont have any argument for (1) but for (2) I can say that we have something like this if we convert the circles in mathematical notation:

L2. L2' and L1.L', both of them are equal to phi but in the next line they are writing L1 is a subset of L2 and L2 is a subset of L1.

Zulfi.