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Mirrors > Home > ILE Home > Th. List > coss2 | Unicode version |
Description: Subclass theorem for composition. (Contributed by NM, 5-Apr-2013.) |
Ref | Expression |
---|---|
coss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . . . . . 6 | |
2 | 1 | ssbrd 3805 | . . . . 5 |
3 | 2 | anim1d 319 | . . . 4 |
4 | 3 | eximdv 1760 | . . 3 |
5 | 4 | ssopab2dv 4015 | . 2 |
6 | df-co 4354 | . 2 | |
7 | df-co 4354 | . 2 | |
8 | 5, 6, 7 | 3sstr4g 2986 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wex 1381 wss 2917 class class class wbr 3764 copab 3817 ccom 4349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-in 2924 df-ss 2931 df-br 3765 df-opab 3819 df-co 4354 |
This theorem is referenced by: coeq2 4494 funss 4920 tposss 5861 dftpos4 5878 |
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