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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 4009 | . . . . 5 |
3 | 2 | anim1d 334 | . . . 4 |
4 | 3 | eximdv 1860 | . . 3 |
5 | 4 | ssopab2dv 4240 | . 2 |
6 | df-co 4597 | . 2 | |
7 | df-co 4597 | . 2 | |
8 | 5, 6, 7 | 3sstr4g 3171 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1472 wss 3102 class class class wbr 3967 copab 4026 ccom 4592 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-in 3108 df-ss 3115 df-br 3968 df-opab 4028 df-co 4597 |
This theorem is referenced by: coeq2 4746 funss 5191 tposss 6195 dftpos4 6212 |
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