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Math Help - is this procedure right in proving a logical equivalence?

  1. #1
    Member Jskid's Avatar
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    is this procedure right in proving a logical equivalence?

    \Leftrightarrow

    Suppose someone wanted to prove a \Leftrightarrow z and they proceeded as follows:
    a \Leftrightarrow z
    b \Leftrightarrow y
    c \Leftrightarrow x
    ...
    m \Leftrightarrow m
    Is there a problem with this?

    I think yes because the intermediate steps to the proof are wrong, so it's like the premises being wrong?

    Edit: suppose all intermediate steps are correct as in the next line follows the former.
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  2. #2
    MHF Contributor
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    Re: is this procedure right in proving a logical equivalence?

    If each line implies the previous line, then this is a valid proof of a <=> z.
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