Description: Base set of an opposite category. (Contributed by Mario Carneiro, 2-Jan-2017) (Proof shortened by AV, 18-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | oppcbas.1 | |
|
oppcbas.2 | |
||
Assertion | oppcbas | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oppcbas.1 | |
|
2 | oppcbas.2 | |
|
3 | baseid | |
|
4 | slotsbhcdif | |
|
5 | 4 | simp1i | |
6 | 3 5 | setsnid | |
7 | 4 | simp2i | |
8 | 3 7 | setsnid | |
9 | 6 8 | eqtri | |
10 | eqid | |
|
11 | eqid | |
|
12 | eqid | |
|
13 | 10 11 12 1 | oppcval | |
14 | 13 | fveq2d | |
15 | 9 14 | eqtr4id | |
16 | base0 | |
|
17 | 16 | eqcomi | |
18 | 17 1 | fveqprc | |
19 | 15 18 | pm2.61i | |
20 | 2 19 | eqtri | |