Description: .r is unaffected by restriction. (Contributed by Stefan O'Rear, 27-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressmulr.1 | |- S = ( R |`s A ) |
|
ressmulr.2 | |- .x. = ( .r ` R ) |
||
Assertion | ressmulr | |- ( A e. V -> .x. = ( .r ` S ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressmulr.1 | |- S = ( R |`s A ) |
|
2 | ressmulr.2 | |- .x. = ( .r ` R ) |
|
3 | df-mulr | |- .r = Slot 3 |
|
4 | 3nn | |- 3 e. NN |
|
5 | 1lt3 | |- 1 < 3 |
|
6 | 1 2 3 4 5 | resslem | |- ( A e. V -> .x. = ( .r ` S ) ) |