Description: An identity theorem for substitution. Remark 9.1 in Megill p. 447 (p. 15 of the preprint). (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 30-Sep-2018)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbid | |- ( [ x / x ] ph <-> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equid | |- x = x |
|
| 2 | sbequ12r | |- ( x = x -> ( [ x / x ] ph <-> ph ) ) |
|
| 3 | 1 2 | ax-mp | |- ( [ x / x ] ph <-> ph ) |