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Mirrors > Home > MPE Home > Th. List > brco | Structured version Visualization version Unicode version |
Description: Binary relation on a composition. (Contributed by NM, 21-Sep-2004.) (Revised by Mario Carneiro, 24-Feb-2015.) |
Ref | Expression |
---|---|
opelco.1 | |
opelco.2 |
Ref | Expression |
---|---|
brco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelco.1 | . 2 | |
2 | opelco.2 | . 2 | |
3 | brcog 5288 | . 2 | |
4 | 1, 2, 3 | mp2an 708 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wcel 1990 cvv 3200 class class class wbr 4653 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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-co 5123 |
This theorem is referenced by: opelco 5293 cnvco 5308 resco 5639 imaco 5640 rnco 5641 coass 5654 dffv2 6271 foeqcnvco 6555 f1eqcocnv 6556 rtrclreclem3 13800 imasleval 16201 ustuqtop4 22048 metustexhalf 22361 dftr6 31640 coep 31641 coepr 31642 dfpo2 31645 brtxp 31987 pprodss4v 31991 brpprod 31992 sscoid 32020 elfuns 32022 brimg 32044 brapply 32045 brcup 32046 brcap 32047 brsuccf 32048 funpartlem 32049 brrestrict 32056 dfrecs2 32057 dfrdg4 32058 cnvssco 37912 |
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