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Mirrors > Home > MPE Home > Th. List > enfii | Structured version Visualization version 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 8176 | . 2 | |
2 | 1 | biimparc 504 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 class class class wbr 4653 cen 7952 cfn 7955 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-er 7742 df-en 7956 df-fin 7959 |
This theorem is referenced by: domfi 8181 en1eqsn 8190 isfinite2 8218 xpfi 8231 fofinf1o 8241 cnvfi 8248 f1dmvrnfibi 8250 pwfi 8261 cantnfcl 8564 en2eqpr 8830 fzfi 12771 hasheni 13136 fz1isolem 13245 isercolllem2 14396 isercoll 14398 summolem2a 14446 summolem2 14447 zsum 14449 prodmolem2a 14664 prodmolem2 14665 zprod 14667 bitsf1 15168 orbsta2 17747 ovoliunlem1 23270 wlksnfi 26802 eupthfi 27065 eulerpartlemgs2 30442 derangenlem 31153 erdsze2lem2 31186 heicant 33444 |
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