Thread: derive formulas in mathematical logic

Hey everyone,

Here's the problem:

Show that if and , then

I soooort of know how to start, it's supposed to be like,
We already have a derivation of from , so start with:
.
.
.
(k)
(k+1)
(k+2)
.
.
.

I have a hard time getting this naturally, because to me it feels like I should be able to assume in line (k+1) and then have ... but then, that's not right because it doesn't use Modus Ponens or any of the three axioms.

Any help or hints as to how I should be thinking?

Originally Posted by sfitz

Hey everyone,

Here's the problem:

Show that if and , then

I soooort of know how to start, it's supposed to be like,
We already have a derivation of from , so start with:
.
.
.
(k)
(k+1)
(k+2)
.
.
.

I have a hard time getting this naturally, because to me it feels like I should be able to assume in line (k+1) and then have ... but then, that's not right because it doesn't use Modus Ponens or any of the three axioms.

Any help or hints as to how I should be thinking?

From what you've described (three axioms schemes, and one rule that you've identified as MP), I'd say you might be thinking:

First, an application of the Deduction Theorem, followed by an application of MP.