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Mirrors > Home > MPE Home > Th. List > df-co | Structured version Visualization version Unicode version |
Description: Define the composition of two classes. Definition 6.6(3) of [TakeutiZaring] p. 24. For example, (ex-co 27295) because (see cos0 14880) and (see df-e 14799). Note that Definition 7 of [Suppes] p. 63 reverses and , uses instead of , and calls the operation "relative product." (Contributed by NM, 4-Jul-1994.) |
Ref | Expression |
---|---|
df-co |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | cB | . . 3 | |
3 | 1, 2 | ccom 5118 | . 2 |
4 | vx | . . . . . . 7 | |
5 | 4 | cv 1482 | . . . . . 6 |
6 | vz | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | 5, 7, 2 | wbr 4653 | . . . . 5 |
9 | vy | . . . . . . 7 | |
10 | 9 | cv 1482 | . . . . . 6 |
11 | 7, 10, 1 | wbr 4653 | . . . . 5 |
12 | 8, 11 | wa 384 | . . . 4 |
13 | 12, 6 | wex 1704 | . . 3 |
14 | 13, 4, 9 | copab 4712 | . 2 |
15 | 3, 14 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: coss1 5277 coss2 5278 nfco 5287 brcog 5288 cnvco 5308 cotrg 5507 relco 5633 coundi 5636 coundir 5637 cores 5638 xpco 5675 dffun2 5898 funco 5928 xpcomco 8050 coss12d 13711 xpcogend 13713 trclublem 13734 rtrclreclem3 13800 |
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