Description: Conversion of implicit substitution to explicit substitution (deduction version of sbie ). Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker sbiedvw when possible. (Contributed by NM, 7-Jan-2017) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbiedv.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
| Assertion | sbiedv | |- ( ph -> ( [ y / x ] ps <-> ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbiedv.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
| 2 | nfv | |- F/ x ph |
|
| 3 | nfvd | |- ( ph -> F/ x ch ) |
|
| 4 | 1 | ex | |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) |
| 5 | 2 3 4 | sbied | |- ( ph -> ( [ y / x ] ps <-> ch ) ) |