Fitch proof for a=b Good evening! I have got a question about identities in Fitch. Given: $a = b$ To prove: $b = a$ Is the identity in fitch bidirectional, so I can just replace both with both? Or do I have to do something like this and if yes, is this legit?: $a = b$ $a = a$ \ =-intro $b = a$ \ =-Elim: 1 Thank you very much

$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\\\hline#2\end{array}}$

Yes, that is okay. You do not need to substitute every occurance of the replaced term. $$\fitch{[a, b]}{\fitch{~~1.~~a=b}{~~2.~~a=a\qquad{=}\mathsf {intro}\\\~~3.~~b=a\qquad{=}\textsf{elim }2,1\quad\because~\color{red}a=a,a\color{red}=b\vdash \color{red}b=a}\\\~~4.~~a=b\to b=a}$$