Description: The set of indexed edges of an extensible structure with (at least) two slots. (Contributed by AV, 12-Oct-2020) (Revised by AV, 7-Jun-2021) (Revised by AV, 12-Nov-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | funiedgdmge2val | |- ( ( Fun ( G \ { (/) } ) /\ 2 <_ ( # ` dom G ) ) -> ( iEdg ` G ) = ( .ef ` G ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iedgval | |- ( iEdg ` G ) = if ( G e. ( _V X. _V ) , ( 2nd ` G ) , ( .ef ` G ) ) |
|
| 2 | fundmge2nop0 | |- ( ( Fun ( G \ { (/) } ) /\ 2 <_ ( # ` dom G ) ) -> -. G e. ( _V X. _V ) ) |
|
| 3 | 2 | iffalsed | |- ( ( Fun ( G \ { (/) } ) /\ 2 <_ ( # ` dom G ) ) -> if ( G e. ( _V X. _V ) , ( 2nd ` G ) , ( .ef ` G ) ) = ( .ef ` G ) ) |
| 4 | 1 3 | syl5eq | |- ( ( Fun ( G \ { (/) } ) /\ 2 <_ ( # ` dom G ) ) -> ( iEdg ` G ) = ( .ef ` G ) ) |