Description: The base set of a restriction is a subset of the base set of the original structure. (Contributed by Stefan O'Rear, 27-Nov-2014) (Revised by Mario Carneiro, 30-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ressbas.r | |
|
ressbas.b | |
||
Assertion | ressbasss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressbas.r | |
|
2 | ressbas.b | |
|
3 | 1 2 | ressbas | |
4 | inss2 | |
|
5 | 3 4 | eqsstrrdi | |
6 | reldmress | |
|
7 | 6 | ovprc2 | |
8 | 1 7 | eqtrid | |
9 | 8 | fveq2d | |
10 | base0 | |
|
11 | 0ss | |
|
12 | 10 11 | eqsstrri | |
13 | 9 12 | eqsstrdi | |
14 | 5 13 | pm2.61i | |