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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 2189 |
. . 3
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4 | en3d.3 |
. . . 4
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5 | 4 | imp 124 |
. . 3
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6 | en3d.4 |
. . . 4
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7 | 6 | imp 124 |
. . 3
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8 | en3d.5 |
. . . 4
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9 | 8 | imp 124 |
. . 3
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10 | 3, 5, 7, 9 | f1o2d 6100 |
. 2
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11 | f1oen2g 6782 |
. 2
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12 | 1, 2, 10, 11 | syl3anc 1249 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 df-en 6768 |
This theorem is referenced by: en3i 6798 fundmen 6833 mapen 6875 mapxpen 6877 ssenen 6880 fzen 10075 uzennn 10469 hashfacen 10851 hashdvds 12256 |
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