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Mirrors > Home > MPE Home > Th. List > df-prf | Structured version Visualization version Unicode version |
Description: Define the pairing operation for functors (which takes two functors and and produces 〈,〉F c ). (Contributed by Mario Carneiro, 11-Jan-2017.) |
Ref | Expression |
---|---|
df-prf | 〈,〉F |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cprf 16811 | . 2 〈,〉F | |
2 | vf | . . 3 | |
3 | vg | . . 3 | |
4 | cvv 3200 | . . 3 | |
5 | vb | . . . 4 | |
6 | 2 | cv 1482 | . . . . . 6 |
7 | c1st 7166 | . . . . . 6 | |
8 | 6, 7 | cfv 5888 | . . . . 5 |
9 | 8 | cdm 5114 | . . . 4 |
10 | vx | . . . . . 6 | |
11 | 5 | cv 1482 | . . . . . 6 |
12 | 10 | cv 1482 | . . . . . . . 8 |
13 | 12, 8 | cfv 5888 | . . . . . . 7 |
14 | 3 | cv 1482 | . . . . . . . . 9 |
15 | 14, 7 | cfv 5888 | . . . . . . . 8 |
16 | 12, 15 | cfv 5888 | . . . . . . 7 |
17 | 13, 16 | cop 4183 | . . . . . 6 |
18 | 10, 11, 17 | cmpt 4729 | . . . . 5 |
19 | vy | . . . . . 6 | |
20 | vh | . . . . . . 7 | |
21 | 19 | cv 1482 | . . . . . . . . 9 |
22 | c2nd 7167 | . . . . . . . . . 10 | |
23 | 6, 22 | cfv 5888 | . . . . . . . . 9 |
24 | 12, 21, 23 | co 6650 | . . . . . . . 8 |
25 | 24 | cdm 5114 | . . . . . . 7 |
26 | 20 | cv 1482 | . . . . . . . . 9 |
27 | 26, 24 | cfv 5888 | . . . . . . . 8 |
28 | 14, 22 | cfv 5888 | . . . . . . . . . 10 |
29 | 12, 21, 28 | co 6650 | . . . . . . . . 9 |
30 | 26, 29 | cfv 5888 | . . . . . . . 8 |
31 | 27, 30 | cop 4183 | . . . . . . 7 |
32 | 20, 25, 31 | cmpt 4729 | . . . . . 6 |
33 | 10, 19, 11, 11, 32 | cmpt2 6652 | . . . . 5 |
34 | 18, 33 | cop 4183 | . . . 4 |
35 | 5, 9, 34 | csb 3533 | . . 3 |
36 | 2, 3, 4, 4, 35 | cmpt2 6652 | . 2 |
37 | 1, 36 | wceq 1483 | 1 〈,〉F |
Colors of variables: wff setvar class |
This definition is referenced by: prfval 16839 |
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