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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2660 |
. . . . 5
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2 | vex 2660 |
. . . . 5
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3 | 1, 2 | brcnv 4682 |
. . . 4
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4 | 3 | exbii 1567 |
. . 3
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5 | 4 | abbii 2230 |
. 2
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6 | dfrn2 4687 |
. 2
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7 | df-dm 4509 |
. 2
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8 | 5, 6, 7 | 3eqtr4ri 2146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-opab 3950 df-cnv 4507 df-dm 4509 df-rn 4510 |
This theorem is referenced by: dmcnvcnv 4723 rncnvcnv 4724 rncoeq 4770 cnvimass 4860 cnvimarndm 4861 dminxp 4941 cnvsn0 4965 rnsnopg 4975 dmmpt 4992 dmco 5005 cores2 5009 cnvssrndm 5018 cocnvres 5021 unidmrn 5029 dfdm2 5031 cnvexg 5034 funimacnv 5157 foimacnv 5341 funcocnv2 5348 fimacnv 5503 f1opw2 5930 fopwdom 6683 sbthlemi4 6800 exmidfodomrlemim 7005 |
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