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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 4024 | . . . . 5 |
3 | 2 | anim1d 334 | . . . 4 |
4 | 3 | eximdv 1868 | . . 3 |
5 | 4 | ssopab2dv 4255 | . 2 |
6 | df-co 4612 | . 2 | |
7 | df-co 4612 | . 2 | |
8 | 5, 6, 7 | 3sstr4g 3184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1480 wss 3115 class class class wbr 3981 copab 4041 ccom 4607 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2296 df-in 3121 df-ss 3128 df-br 3982 df-opab 4043 df-co 4612 |
This theorem is referenced by: coeq2 4761 funss 5206 tposss 6210 dftpos4 6227 |
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