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Mirrors > Home > ILE Home > Th. List > ecdmn0m | Unicode version |
Description: A representative of an inhabited equivalence class belongs to the domain of the equivalence relation. (Contributed by Jim Kingdon, 21-Aug-2019.) |
Ref | Expression |
---|---|
ecdmn0m |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2666 |
. 2
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2 | ecexr 6386 |
. . 3
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3 | 2 | exlimiv 1558 |
. 2
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4 | eldmg 4692 |
. . 3
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5 | vex 2658 |
. . . . 5
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6 | elecg 6419 |
. . . . 5
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7 | 5, 6 | mpan 418 |
. . . 4
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8 | 7 | exbidv 1777 |
. . 3
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9 | 4, 8 | bitr4d 190 |
. 2
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10 | 1, 3, 9 | pm5.21nii 676 |
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 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-sbc 2877 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-br 3894 df-opab 3948 df-xp 4503 df-cnv 4505 df-dm 4507 df-rn 4508 df-res 4509 df-ima 4510 df-ec 6383 |
This theorem is referenced by: ereldm 6424 elqsn0m 6449 ecelqsdm 6451 |
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