Description: Change bound variables in an indexed intersection. (Contributed by Jeff Hankins, 26-Aug-2009) Add disjoint variable condition to avoid ax-13 . See cbviinvg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbviunv.1 | |- ( x = y -> B = C ) |
|
| Assertion | cbviinv | |- |^|_ x e. A B = |^|_ y e. A C |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbviunv.1 | |- ( x = y -> B = C ) |
|
| 2 | nfcv | |- F/_ y B |
|
| 3 | nfcv | |- F/_ x C |
|
| 4 | 2 3 1 | cbviin | |- |^|_ x e. A B = |^|_ y e. A C |