Description: Obsolete version of sucdom as of 4-Dec-2024. (Contributed by Mario Carneiro, 12-Jan-2013) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sucdomOLD | |- ( A e. _om -> ( A ~< B <-> suc A ~<_ B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sucdom2 | |- ( A ~< B -> suc A ~<_ B ) |
|
| 2 | php4 | |- ( A e. _om -> A ~< suc A ) |
|
| 3 | sdomdomtr | |- ( ( A ~< suc A /\ suc A ~<_ B ) -> A ~< B ) |
|
| 4 | 3 | ex | |- ( A ~< suc A -> ( suc A ~<_ B -> A ~< B ) ) |
| 5 | 2 4 | syl | |- ( A e. _om -> ( suc A ~<_ B -> A ~< B ) ) |
| 6 | 1 5 | impbid2 | |- ( A e. _om -> ( A ~< B <-> suc A ~<_ B ) ) |