Für ${\displaystyle {}\alpha }$ betrachten wir den Ausdruck ${\displaystyle {}x_{1}=x_{2}}$ und wir setzen ${\displaystyle {}t_{1}:=x_{2}}$ und ${\displaystyle {}t_{2}:=x_{1}}$. Dann ist einerseits (wir schreiben ${\displaystyle {}\equiv }$ für die Gleichheit von Ausdrücken)

${\displaystyle {}{\begin{aligned}{\left(\alpha {\frac {t_{1}}{x_{1}}}\right)}{\frac {t_{2}}{x_{2}}}&\equiv {\left((x_{1}=x_{2}){\frac {x_{2}}{x_{1}}}\right)}{\frac {x_{1}}{x_{2}}}\\&\equiv {\left(x_{2}=x_{2}\right)}{\frac {x_{1}}{x_{2}}}\\&\equiv x_{1}=x_{1},\end{aligned}}}$

was allgemeingültig ist, und andererseits

${\displaystyle {}{\begin{aligned}\alpha {\frac {t_{1},t_{2}}{x_{1},x_{2}}}&\equiv (x_{1}=x_{2}){\frac {x_{2},x_{1}}{x_{1},x_{2}}}\\&\equiv (x_{1}{\frac {x_{2},x_{1}}{x_{1},x_{2}}}=x_{2}{\frac {x_{2},x_{1}}{x_{1},x_{2}}})\\&\equiv x_{2}=x_{1},\end{aligned}}}$

was nicht allgemeingültig ist. Somit ist

${\displaystyle x_{1}=x_{1}\rightarrow x_{2}=x_{1}}$