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Math Help - Formal Logic Proof

  1. #1
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    Formal Logic Proof

    Hello.

    I posted this on math help boards:

    (http:///f15/formal-logic-proof-3601/#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  \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)  \forall x (0' + x' ) = (x . 0'') Assumption
    1 (2) (0' +x')=(x.0'') Universal Elimination rule
    1 (3) \exists y (y+x')=(x.y') Existential Introduction, 2
    4 (4)  y=x Assumption
    1,4 (5)  \exists x (x+x')=(x.x') Taut 3,4 <--- ?
    1 (6)  \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?
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  2. #2
    MHF Contributor
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    Re: Formal Logic Proof

    Answered on MHB.
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