Description: 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.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sb9i | |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sb9 | |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph ) |
|
| 2 | 1 | biimpi | |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph ) |