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Mirrors > Home > MPE Home > Th. List > brres | Structured version Visualization version Unicode version |
Description: Binary relation on a restriction. (Contributed by NM, 12-Dec-2006.) |
Ref | Expression |
---|---|
opelres.1 |
Ref | Expression |
---|---|
brres |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelres.1 | . . 3 | |
2 | 1 | opelres 5401 | . 2 |
3 | df-br 4654 | . 2 | |
4 | df-br 4654 | . . 3 | |
5 | 4 | anbi1i 731 | . 2 |
6 | 2, 3, 5 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wcel 1990 cvv 3200 cop 4183 class class class wbr 4653 cres 5116 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 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-xp 5120 df-res 5126 |
This theorem is referenced by: dfres2 5453 dfima2 5468 poirr2 5520 cores 5638 resco 5639 rnco 5641 fnres 6007 fvres 6207 nfunsn 6225 1stconst 7265 2ndconst 7266 fsplit 7282 wfrlem5 7419 dprd2da 18441 metustid 22359 dvres 23675 dvres2 23676 ltgov 25492 axhcompl-zf 27855 hlimadd 28050 hhcmpl 28057 hhcms 28060 hlim0 28092 dfpo2 31645 eqfunresadj 31659 dfdm5 31676 dfrn5 31677 frrlem5 31784 txpss3v 31985 brtxp 31987 pprodss4v 31991 brpprod 31992 brimg 32044 brapply 32045 funpartfun 32050 dfrdg4 32058 xrnss3v 34135 funressnfv 41208 dfdfat2 41211 setrec2lem2 42441 |
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