There is a representable relation Sb1 such that for a formula $\displaystyle \alpha$, variable $\displaystyle x$, and term $\displaystyle t$, $\displaystyle <\sharp \alpha ,\sharp x,\sharp t> \in \text{Sb1}$ iff $\displaystyle t$ is substitutable for $\displaystyle x$ in $\displaystyle \alpha$.

The necessary definitions can be found in

http://cs.nyu.edu/courses/fall03/G22...c/lec12_h4.pdf (slide 6, 9)

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t is substitutable for x in $\displaystyle \alpha$ if $\displaystyle \alpha$ is an atomic formula, and so on (Enderton p 113).

How do I prove this problem using the definition of "t is substitutable for x in $\displaystyle \alpha$"?

Thanks.