Description: The group addition operation as a function. (Contributed by Mario Carneiro, 14-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | plusffval.1 | |- B = ( Base ` G ) |
|
plusffval.2 | |- .+ = ( +g ` G ) |
||
plusffval.3 | |- .+^ = ( +f ` G ) |
||
Assertion | plusfval | |- ( ( X e. B /\ Y e. B ) -> ( X .+^ Y ) = ( X .+ Y ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | plusffval.1 | |- B = ( Base ` G ) |
|
2 | plusffval.2 | |- .+ = ( +g ` G ) |
|
3 | plusffval.3 | |- .+^ = ( +f ` G ) |
|
4 | oveq12 | |- ( ( x = X /\ y = Y ) -> ( x .+ y ) = ( X .+ Y ) ) |
|
5 | 1 2 3 | plusffval | |- .+^ = ( x e. B , y e. B |-> ( x .+ y ) ) |
6 | ovex | |- ( X .+ Y ) e. _V |
|
7 | 4 5 6 | ovmpoa | |- ( ( X e. B /\ Y e. B ) -> ( X .+^ Y ) = ( X .+ Y ) ) |