
Formal Logic Proof
Hello.
I posted this on math help boards:
(http:///f15/formallogicproof3601/#post15926)
...but I didn't know how active that site was. Feel free to reply on there as well as here.
This is my question:
Give a formal proof to show $\displaystyle \forall x (0' + x' ) = (x . 0'') \vdash \exists x (x + x')= (x . x')$
I'm new to these, and this one looks like it should be easy.
What I want to do is:
1). substitute x into where there are already x's.
2). Make the statement valid for all y
3). substitute y into 0' and y' into 0''.
3). Since it's valid for all y, choose y to be 0.
Here's what I did:
1 (1) $\displaystyle \forall x (0' + x' ) = (x . 0'')$ Assumption
1 (2) $\displaystyle (0' +x')=(x.0'')$ Universal Elimination rule
1 (3) $\displaystyle \exists y (y+x')=(x.y') $ Existential Introduction, 2
4 (4) $\displaystyle y=x $ Assumption
1,4 (5) $\displaystyle \exists x (x+x')=(x.x') $ Taut 3,4 < ?
1 (6) $\displaystyle \exists x (x+x')= (x.x') $ Existential Hypothesis, 5
I think i've got the right idea, I think the execution starts to go wrong at around line (4).
Does anyone have any ideas?

Re: Formal Logic Proof