Description: An identity theorem for substitution. See sbid . See Remark 9.1 in Megill p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbidd.1 | |- ( ph -> [ x / x ] ps ) |
|
| Assertion | sbidd | |- ( ph -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbidd.1 | |- ( ph -> [ x / x ] ps ) |
|
| 2 | sbid | |- ( [ x / x ] ps <-> ps ) |
|
| 3 | 1 2 | sylib | |- ( ph -> ps ) |