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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 | |
en3d.2 | |
en3d.3 | |
en3d.4 | |
en3d.5 |
Ref | Expression |
---|---|
en3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en3d.1 | . 2 | |
2 | en3d.2 | . 2 | |
3 | eqid 2139 | . . 3 | |
4 | en3d.3 | . . . 4 | |
5 | 4 | imp 123 | . . 3 |
6 | en3d.4 | . . . 4 | |
7 | 6 | imp 123 | . . 3 |
8 | en3d.5 | . . . 4 | |
9 | 8 | imp 123 | . . 3 |
10 | 3, 5, 7, 9 | f1o2d 5975 | . 2 |
11 | f1oen2g 6649 | . 2 | |
12 | 1, 2, 10, 11 | syl3anc 1216 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cvv 2686 class class class wbr 3929 cmpt 3989 wf1o 5122 cen 6632 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-en 6635 |
This theorem is referenced by: en3i 6665 fundmen 6700 mapen 6740 mapxpen 6742 ssenen 6745 fzen 9823 uzennn 10209 hashfacen 10579 hashdvds 11897 |
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