Description: A composition law for substitution. Version of sbco2 with disjoint variable conditions and fewer axioms. (Contributed by NM, 30-Jun-1994) (Revised by BJ, 22-Dec-2020) (Proof shortened by Wolf Lammen, 29-Apr-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbco2vv | |- ( [ y / z ] [ z / x ] ph <-> [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbequ | |- ( z = w -> ( [ z / x ] ph <-> [ w / x ] ph ) ) |
|
| 2 | sbequ | |- ( w = y -> ( [ w / x ] ph <-> [ y / x ] ph ) ) |
|
| 3 | 1 2 | sbievw2 | |- ( [ y / z ] [ z / x ] ph <-> [ y / x ] ph ) |