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Mirrors > Home > MPE Home > Th. List > opelco | Structured version Visualization version Unicode version |
Description: Ordered pair membership in a composition. (Contributed by NM, 27-Dec-1996.) (Revised by Mario Carneiro, 24-Feb-2015.) |
Ref | Expression |
---|---|
opelco.1 | |
opelco.2 |
Ref | Expression |
---|---|
opelco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4654 | . 2 | |
2 | opelco.1 | . . 3 | |
3 | opelco.2 | . . 3 | |
4 | 2, 3 | brco 5292 | . 2 |
5 | 1, 4 | bitr3i 266 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wcel 1990 cvv 3200 cop 4183 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: dmcoss 5385 dmcosseq 5387 cotrg 5507 coiun 5645 co02 5649 coi1 5651 coass 5654 fmptco 6396 dftpos4 7371 fmptcof2 29457 cnvco1 31649 cnvco2 31650 txpss3v 31985 dffun10 32021 xrnss3v 34135 coiun1 37944 |
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