Description: Alternate proof of 1sdom2 , shorter but requiring ax-un . (Contributed by NM, 4-Apr-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 1sdom2ALT | |- 1o ~< 2o |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1onn | |- 1o e. _om |
|
| 2 | php4 | |- ( 1o e. _om -> 1o ~< suc 1o ) |
|
| 3 | 1 2 | ax-mp | |- 1o ~< suc 1o |
| 4 | df-2o | |- 2o = suc 1o |
|
| 5 | 3 4 | breqtrri | |- 1o ~< 2o |