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Mirrors > Home > ILE Home > Th. List > en3i | Unicode version |
Description: Equinumerosity inference from an implicit one-to-one onto function. (Contributed by NM, 19-Jul-2004.) |
Ref | Expression |
---|---|
en3i.1 | |
en3i.2 | |
en3i.3 | |
en3i.4 | |
en3i.5 |
Ref | Expression |
---|---|
en3i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en3i.1 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | en3i.2 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | en3i.3 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | en3i.4 | . . . 4 | |
8 | 7 | a1i 9 | . . 3 |
9 | en3i.5 | . . . 4 | |
10 | 9 | a1i 9 | . . 3 |
11 | 2, 4, 6, 8, 10 | en3d 6272 | . 2 |
12 | 11 | trud 1293 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wtru 1285 wcel 1433 cvv 2601 class class class wbr 3785 cen 6242 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-en 6245 |
This theorem is referenced by: nn0ennn 9425 |
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