the if part can be written (b -> c) -> a.
Since you can rewrite (b -> c) as (!b | c)
to prove the if part you have to prove
!b -> a
c -> a
I have to show "a" occurs if & only if, whenever "b" occurs, "c" occurs.
For the only if direction I'm pretty sure this means if I have to assume "a" & "b" and then use this to prove "c".
But for the if direction, is it correct that I have to assume "c" & "b" and use this to prove "a"?
Thanks in advance