Description: An equality theorem for substitution. (Contributed by NM, 14-May-1993) (Proof shortened by Wolf Lammen, 15-Sep-2018) (Proof shortened by Steven Nguyen, 7-Jul-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbequi | |- ( x = y -> ( [ x / z ] ph -> [ y / z ] ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbequ | |- ( x = y -> ( [ x / z ] ph <-> [ y / z ] ph ) ) |
|
| 2 | 1 | biimpd | |- ( x = y -> ( [ x / z ] ph -> [ y / z ] ph ) ) |