is this procedure right in proving a logical equivalence?

$\displaystyle \Leftrightarrow$

Suppose someone wanted to prove $\displaystyle a \Leftrightarrow z$ and they proceeded as follows:

$\displaystyle a \Leftrightarrow z$

$\displaystyle b \Leftrightarrow y$

$\displaystyle c \Leftrightarrow x$

...

$\displaystyle m \Leftrightarrow m$

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.

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.