Description: Alternate proof of ru , simplified using (indirectly) the Axiom of Regularity ax-reg . (Contributed by Alan Sare, 4-Oct-2008) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ruALT | |- { x | x e/ x } e/ _V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vprc | |- -. _V e. _V |
|
| 2 | 1 | nelir | |- _V e/ _V |
| 3 | ruv | |- { x | x e/ x } = _V |
|
| 4 | neleq1 | |- ( { x | x e/ x } = _V -> ( { x | x e/ x } e/ _V <-> _V e/ _V ) ) |
|
| 5 | 3 4 | ax-mp | |- ( { x | x e/ x } e/ _V <-> _V e/ _V ) |
| 6 | 2 5 | mpbir | |- { x | x e/ x } e/ _V |