Description: A composition law for substitution. Version of sbco with a disjoint variable condition using fewer axioms. (Contributed by NM, 14-May-1993) (Revised by Gino Giotto, 7-Aug-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbcov | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbcom3vv | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] [ y / y ] ph ) |
|
| 2 | sbid | |- ( [ y / y ] ph <-> ph ) |
|
| 3 | 2 | sbbii | |- ( [ y / x ] [ y / y ] ph <-> [ y / x ] ph ) |
| 4 | 1 3 | bitri | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) |