Description: Obsolete version of cbvmptv as of 17-Nov-2024. (Contributed by Mario Carneiro, 19-Feb-2013) Add disjoint variable condition to avoid ax-13 . See cbvmptvg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 17-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbvmptvOLD.1 | |- ( x = y -> B = C ) |
|
| Assertion | cbvmptvOLD | |- ( x e. A |-> B ) = ( y e. A |-> C ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbvmptvOLD.1 | |- ( x = y -> B = C ) |
|
| 2 | nfcv | |- F/_ y B |
|
| 3 | nfcv | |- F/_ x C |
|
| 4 | 2 3 1 | cbvmpt | |- ( x e. A |-> B ) = ( y e. A |-> C ) |