a) for any
I'm confused about this one because I tried proof by contradiction, so:
(1) by assumption
(2) by assuming the negation of where is also written as
... and then isn't that already a contradiction?
b) where x is not free in
This one I think it must involve axioms 4 and 5 somehow, but I guess that's obvious
c) for any term not involving x
And this one must involve axioms 4 and 6
Derive them using these (for your convenience and my LaTeX practice):
4: ( is a term freely substitutable for x in )
5: (where x is not free in )
As well as Modus Ponens, Generalization, and the Deduction theorem
Any help would be really appreciated!