Description: Hom-sets of the opposite category. (Contributed by Mario Carneiro, 2-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | oppchom.h | |- H = ( Hom ` C ) |
|
oppchom.o | |- O = ( oppCat ` C ) |
||
Assertion | oppchom | |- ( X ( Hom ` O ) Y ) = ( Y H X ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oppchom.h | |- H = ( Hom ` C ) |
|
2 | oppchom.o | |- O = ( oppCat ` C ) |
|
3 | 1 2 | oppchomfval | |- tpos H = ( Hom ` O ) |
4 | 3 | oveqi | |- ( X tpos H Y ) = ( X ( Hom ` O ) Y ) |
5 | ovtpos | |- ( X tpos H Y ) = ( Y H X ) |
|
6 | 4 5 | eqtr3i | |- ( X ( Hom ` O ) Y ) = ( Y H X ) |