Description: le is unaffected by restriction. (Contributed by Mario Carneiro, 3-Nov-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressle.1 | |- W = ( K |`s A ) |
|
ressle.2 | |- .<_ = ( le ` K ) |
||
Assertion | ressle | |- ( A e. V -> .<_ = ( le ` W ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressle.1 | |- W = ( K |`s A ) |
|
2 | ressle.2 | |- .<_ = ( le ` K ) |
|
3 | df-ple | |- le = Slot ; 1 0 |
|
4 | 10nn | |- ; 1 0 e. NN |
|
5 | 1lt10 | |- 1 < ; 1 0 |
|
6 | 1 2 3 4 5 | resslem | |- ( A e. V -> .<_ = ( le ` W ) ) |