[SOLVED] Logic proof which I am having trouble understanding

We have been given the following as an example of a proof, but I can not follow it.

(b(1)=C OR b(1) ≠ C) AND (b(1)=C AND b(2)=J OR b(1)=J AND b(2)=C), (b(1)=C AND b(1) = J)=F

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(b(1)=C AND b(2)=J) OR (b(1) ≠ C) AND (b(1)=J AND b(2)=C)

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b(1) ≠ C OR b(2) = J

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b(1) = C -> b(2) = J

I see what happens from the second to last step but I'm unsure about the rest. Could someone please explain? Thanks