Description: Obsolete version of ralcom4 as of 26-Aug-2023. Commutation of restricted and unrestricted universal quantifiers. (Contributed by NM, 26-Mar-2004) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ralcom4OLD | |- ( A. x e. A A. y ph <-> A. y A. x e. A ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralcom | |- ( A. x e. A A. y e. _V ph <-> A. y e. _V A. x e. A ph ) |
|
2 | ralv | |- ( A. y e. _V ph <-> A. y ph ) |
|
3 | 2 | ralbii | |- ( A. x e. A A. y e. _V ph <-> A. x e. A A. y ph ) |
4 | ralv | |- ( A. y e. _V A. x e. A ph <-> A. y A. x e. A ph ) |
|
5 | 1 3 4 | 3bitr3i | |- ( A. x e. A A. y ph <-> A. y A. x e. A ph ) |