Description: Change the bound variable of a restricted at-most-one quantifier using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Alexander van der Vekens, 17-Jun-2017) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbvrmov.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | cbvrmov | |- ( E* x e. A ph <-> E* y e. A ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbvrmov.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | nfv | |- F/ y ph |
|
| 3 | nfv | |- F/ x ps |
|
| 4 | 2 3 1 | cbvrmo | |- ( E* x e. A ph <-> E* y e. A ps ) |