Theorem sb9i

Commutation of quantification and substitution variables. Usage of this theorem is discouraged because it depends on [ax-13]. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 15-Jun-2019.) (New usage is discouraged.)

Conclusion
\( \vdash \forall x \, [ x / y ] \, \varphi \rightarrow \forall y \, [ y / x ] \, \varphi \)
Proof
sb9
biimpi _