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