Description: comp is unaffected by restriction. (Contributed by Mario Carneiro, 5-Jan-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | resshom.1 | |- D = ( C |`s A ) |
|
| ressco.2 | |- .x. = ( comp ` C ) |
||
| Assertion | ressco | |- ( A e. V -> .x. = ( comp ` D ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resshom.1 | |- D = ( C |`s A ) |
|
| 2 | ressco.2 | |- .x. = ( comp ` C ) |
|
| 3 | df-cco | |- comp = Slot ; 1 5 |
|
| 4 | 1nn0 | |- 1 e. NN0 |
|
| 5 | 5nn | |- 5 e. NN |
|
| 6 | 4 5 | decnncl | |- ; 1 5 e. NN |
| 7 | 1nn | |- 1 e. NN |
|
| 8 | 5nn0 | |- 5 e. NN0 |
|
| 9 | 1lt10 | |- 1 < ; 1 0 |
|
| 10 | 7 8 4 9 | declti | |- 1 < ; 1 5 |
| 11 | 1 2 3 6 10 | resslem | |- ( A e. V -> .x. = ( comp ` D ) ) |