Description: +g is unaffected by restriction. (Contributed by Stefan O'Rear, 27-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressplusg.1 | |- H = ( G |`s A ) |
|
ressplusg.2 | |- .+ = ( +g ` G ) |
||
Assertion | ressplusg | |- ( A e. V -> .+ = ( +g ` H ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressplusg.1 | |- H = ( G |`s A ) |
|
2 | ressplusg.2 | |- .+ = ( +g ` G ) |
|
3 | df-plusg | |- +g = Slot 2 |
|
4 | 2nn | |- 2 e. NN |
|
5 | 1lt2 | |- 1 < 2 |
|
6 | 1 2 3 4 5 | resslem | |- ( A e. V -> .+ = ( +g ` H ) ) |