Description: *r is unaffected by restriction. (Contributed by Mario Carneiro, 9-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressmulr.1 | |- S = ( R |`s A ) |
|
ressstarv.2 | |- .* = ( *r ` R ) |
||
Assertion | ressstarv | |- ( A e. V -> .* = ( *r ` S ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressmulr.1 | |- S = ( R |`s A ) |
|
2 | ressstarv.2 | |- .* = ( *r ` R ) |
|
3 | df-starv | |- *r = Slot 4 |
|
4 | 4nn | |- 4 e. NN |
|
5 | 1lt4 | |- 1 < 4 |
|
6 | 1 2 3 4 5 | resslem | |- ( A e. V -> .* = ( *r ` S ) ) |