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Mirrors > Home > ILE Home > Th. List > en2d | 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 |
---|---|
en2d.1 | |
en2d.2 | |
en2d.3 | |
en2d.4 | |
en2d.5 |
Ref | Expression |
---|---|
en2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en2d.1 | . 2 | |
2 | en2d.2 | . 2 | |
3 | eqid 2040 | . . 3 | |
4 | en2d.3 | . . . 4 | |
5 | 4 | imp 115 | . . 3 |
6 | en2d.4 | . . . 4 | |
7 | 6 | imp 115 | . . 3 |
8 | en2d.5 | . . 3 | |
9 | 3, 5, 7, 8 | f1od 5703 | . 2 |
10 | f1oen2g 6235 | . 2 | |
11 | 1, 2, 9, 10 | syl3anc 1135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 cvv 2557 class class class wbr 3764 cmpt 3818 wf1o 4901 cen 6219 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 df-en 6222 |
This theorem is referenced by: en2i 6250 |
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