Description: Obsolete version of onnev as of 27-May-2024. (Contributed by NM, 16-Jun-2007) (Proof shortened by Mario Carneiro, 10-Jan-2013) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | onnevOLD | |- On =/= _V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snsn0non | |- -. { { (/) } } e. On |
|
2 | snex | |- { { (/) } } e. _V |
|
3 | id | |- ( On = _V -> On = _V ) |
|
4 | 2 3 | eleqtrrid | |- ( On = _V -> { { (/) } } e. On ) |
5 | 4 | necon3bi | |- ( -. { { (/) } } e. On -> On =/= _V ) |
6 | 1 5 | ax-mp | |- On =/= _V |