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Mirrors > Home > MPE Home > Th. List > coss2 | Structured version Visualization version Unicode version |
Description: Subclass theorem for composition. (Contributed by NM, 5-Apr-2013.) |
Ref | Expression |
---|---|
coss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . . . . . 6 | |
2 | 1 | ssbrd 4696 | . . . . 5 |
3 | 2 | anim1d 588 | . . . 4 |
4 | 3 | eximdv 1846 | . . 3 |
5 | 4 | ssopab2dv 5004 | . 2 |
6 | df-co 5123 | . 2 | |
7 | df-co 5123 | . 2 | |
8 | 5, 6, 7 | 3sstr4g 3646 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wex 1704 wss 3574 class class class wbr 4653 copab 4712 ccom 5118 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-co 5123 |
This theorem is referenced by: coeq2 5280 funss 5907 tposss 7353 dftpos4 7371 rtrclreclem4 13801 tsrdir 17238 mvdco 17865 ustex2sym 22020 ustex3sym 22021 ustund 22025 ustneism 22027 trust 22033 utop2nei 22054 neipcfilu 22100 fcoinver 29418 trclubgNEW 37925 trrelsuperrel2dg 37963 |
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