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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 2752 |
. . . . 5
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2 | vex 2752 |
. . . . 5
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3 | 1, 2 | brcnv 4822 |
. . . 4
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4 | 3 | exbii 1615 |
. . 3
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5 | 4 | abbii 2303 |
. 2
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6 | dfrn2 4827 |
. 2
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7 | df-dm 4648 |
. 2
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8 | 5, 6, 7 | 3eqtr4ri 2219 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-cnv 4646 df-dm 4648 df-rn 4649 |
This theorem is referenced by: dmcnvcnv 4863 rncnvcnv 4864 rncoeq 4912 cnvimass 5003 cnvimarndm 5004 dminxp 5085 cnvsn0 5109 rnsnopg 5119 dmmpt 5136 dmco 5149 cores2 5153 cnvssrndm 5162 cocnvres 5165 unidmrn 5173 dfdm2 5175 cnvexg 5178 funimacnv 5304 foimacnv 5491 funcocnv2 5498 fimacnv 5658 f1opw2 6090 fopwdom 6849 sbthlemi4 6972 exmidfodomrlemim 7213 hmeores 14086 |
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