Description: Alternate proof of elirrv , shorter but using more axioms. (Contributed by BTernaryTau, 28-Dec-2025) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elirrvALT | |- -. x e. x |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zfregfr | |- _E Fr x |
|
| 2 | efrirr | |- ( _E Fr x -> -. x e. x ) |
|
| 3 | 1 2 | ax-mp | |- -. x e. x |