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 GG, 7-Aug-2023) (Proof shortened by SN, 26-Aug-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbcov | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbequ12r | |- ( x = y -> ( [ x / y ] ph <-> ph ) ) |
|
| 2 | 1 | sbbiiev | |- ( [ y / x ] [ x / y ] ph <-> [ y / x ] ph ) |