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Mirrors > Home > ILE Home > Th. List > enfii | Unicode version |
Description: A set equinumerous to a finite set is finite. (Contributed by Mario Carneiro, 12-Mar-2015.) |
Ref | Expression |
---|---|
enfii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | enfi 6767 | . 2 | |
2 | 1 | biimparc 297 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 class class class wbr 3929 cen 6632 cfn 6634 |
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-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-er 6429 df-en 6635 df-fin 6637 |
This theorem is referenced by: dif1en 6773 diffisn 6787 xpfi 6818 fisseneq 6820 fundmfi 6826 relcnvfi 6829 f1ofi 6831 f1dmvrnfibi 6832 f1finf1o 6835 en1eqsn 6836 exmidonfinlem 7049 fzfig 10203 hashennnuni 10525 hashennn 10526 summodclem2 11151 zsumdc 11153 prodmodclem2 11346 |
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