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Mirrors > Home > ILE Home > Th. List > en3d | Unicode version |
Description: Equinumerosity inference from an implicit one-to-one onto function. (Contributed by NM, 27-Jul-2004.) (Revised by Mario Carneiro, 12-May-2014.) |
Ref | Expression |
---|---|
en3d.1 |
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en3d.2 |
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en3d.3 |
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en3d.4 |
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en3d.5 |
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Ref | Expression |
---|---|
en3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en3d.1 |
. 2
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2 | en3d.2 |
. 2
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3 | eqid 2089 |
. . 3
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4 | en3d.3 |
. . . 4
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5 | 4 | imp 123 |
. . 3
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6 | en3d.4 |
. . . 4
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7 | 6 | imp 123 |
. . 3
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8 | en3d.5 |
. . . 4
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9 | 8 | imp 123 |
. . 3
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10 | 3, 5, 7, 9 | f1o2d 5863 |
. 2
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11 | f1oen2g 6526 |
. 2
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12 | 1, 2, 10, 11 | syl3anc 1175 |
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 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-un 4269 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-mpt 3907 df-id 4129 df-xp 4457 df-rel 4458 df-cnv 4459 df-co 4460 df-dm 4461 df-rn 4462 df-fun 5030 df-fn 5031 df-f 5032 df-f1 5033 df-fo 5034 df-f1o 5035 df-en 6512 |
This theorem is referenced by: en3i 6542 fundmen 6577 mapen 6616 mapxpen 6618 ssenen 6621 fzen 9511 hashfacen 10295 hashdvds 11529 |
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