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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 2663 | . . . . 5 | |
2 | vex 2663 | . . . . 5 | |
3 | 1, 2 | brcnv 4692 | . . . 4 |
4 | 3 | exbii 1569 | . . 3 |
5 | 4 | abbii 2233 | . 2 |
6 | dfrn2 4697 | . 2 | |
7 | df-dm 4519 | . 2 | |
8 | 5, 6, 7 | 3eqtr4ri 2149 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wex 1453 cab 2103 class class class wbr 3899 ccnv 4508 cdm 4509 crn 4510 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-cnv 4517 df-dm 4519 df-rn 4520 |
This theorem is referenced by: dmcnvcnv 4733 rncnvcnv 4734 rncoeq 4782 cnvimass 4872 cnvimarndm 4873 dminxp 4953 cnvsn0 4977 rnsnopg 4987 dmmpt 5004 dmco 5017 cores2 5021 cnvssrndm 5030 cocnvres 5033 unidmrn 5041 dfdm2 5043 cnvexg 5046 funimacnv 5169 foimacnv 5353 funcocnv2 5360 fimacnv 5517 f1opw2 5944 fopwdom 6698 sbthlemi4 6816 exmidfodomrlemim 7025 hmeores 12411 |
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