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Mirrors > Home > ILE Home > Th. List > dfdm4 | Unicode version |
Description: Alternate definition of domain. (Contributed by NM, 28-Dec-1996.) |
Ref | Expression |
---|---|
dfdm4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2724 | . . . . 5 | |
2 | vex 2724 | . . . . 5 | |
3 | 1, 2 | brcnv 4781 | . . . 4 |
4 | 3 | exbii 1592 | . . 3 |
5 | 4 | abbii 2280 | . 2 |
6 | dfrn2 4786 | . 2 | |
7 | df-dm 4608 | . 2 | |
8 | 5, 6, 7 | 3eqtr4ri 2196 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wex 1479 cab 2150 class class class wbr 3976 ccnv 4597 cdm 4598 crn 4599 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-cnv 4606 df-dm 4608 df-rn 4609 |
This theorem is referenced by: dmcnvcnv 4822 rncnvcnv 4823 rncoeq 4871 cnvimass 4961 cnvimarndm 4962 dminxp 5042 cnvsn0 5066 rnsnopg 5076 dmmpt 5093 dmco 5106 cores2 5110 cnvssrndm 5119 cocnvres 5122 unidmrn 5130 dfdm2 5132 cnvexg 5135 funimacnv 5258 foimacnv 5444 funcocnv2 5451 fimacnv 5608 f1opw2 6038 fopwdom 6793 sbthlemi4 6916 exmidfodomrlemim 7148 hmeores 12862 |
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