Convert Conjunctive normal form to disjunctive normal form

[rootmeister64]

Hello,

I have the following formula in CNF:


If I negate this formula twice, I can convert this formula to DNF.
The next three steps are clear to me:

However there is one more step that I do not understand:


De Morgan's law has been used to get from step 2 to step 3. However, I do not understand the method used to get from step 3 to step 4.
My question is: Which method has been used to get from step 3 to step 4?

I would be very grateful if someone could explain the method that has been used to negate the formula in step 3.
Thank you very much!

 

[lex]

Very briefly, in your second-last line, the outer bracket contains an expression in full disjunctive normal form, containing 2 of the 8 possible combinations of the 3 variables or their negations. Therefore the negation of this is simply the disjunction of the other 6 possible combinations! (Your final line).
Hope this helps. If you need any clarification, that's OK.

 

[rootmeister64]

Very briefly, in your second-last line, the outer bracket contains an expression in full disjunctive normal form, containing 2 of the 8 possible combinations of the 3 variables or their negations. Therefore the negation of this is simply the disjunction of the other 6 possible combinations! (Your final line).
Hope this helps. If you need any clarification, that's OK.

Thank you very much! Now I understand the last step.

 

[lex]

Great. No problem.