Description: The universal class is not a member of itself (and thus is not a set). Proposition 5.21 of TakeutiZaring p. 21; our proof, however, does not depend on the Axiom of Regularity. (Contributed by NM, 23-Aug-1993)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | vprc | |- -. _V e. _V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vnex | |- -. E. x x = _V |
|
| 2 | isset | |- ( _V e. _V <-> E. x x = _V ) |
|
| 3 | 1 2 | mtbir | |- -. _V e. _V |