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Mirrors > Home > ILE Home > Th. List > isfi | Unicode version |
Description: Express " is finite." Definition 10.29 of [TakeutiZaring] p. 91 (whose " " is a predicate instead of a class). (Contributed by NM, 22-Aug-2008.) |
Ref | Expression |
---|---|
isfi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fin 6247 | . . 3 | |
2 | 1 | eleq2i 2145 | . 2 |
3 | relen 6248 | . . . . 5 | |
4 | 3 | brrelexi 4402 | . . . 4 |
5 | 4 | rexlimivw 2473 | . . 3 |
6 | breq1 3788 | . . . 4 | |
7 | 6 | rexbidv 2369 | . . 3 |
8 | 5, 7 | elab3 2745 | . 2 |
9 | 2, 8 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 103 wceq 1284 wcel 1433 cab 2067 wrex 2349 cvv 2601 class class class wbr 3785 com 4331 cen 6242 cfn 6244 |
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-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 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 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-br 3786 df-opab 3840 df-xp 4369 df-rel 4370 df-en 6245 df-fin 6247 |
This theorem is referenced by: snfig 6314 fidceq 6354 nnfi 6357 enfi 6358 ssfilem 6360 php5fin 6366 fisbth 6367 fin0 6369 fin0or 6370 diffitest 6371 findcard 6372 findcard2 6373 findcard2s 6374 diffisn 6377 fientri3 6381 unsnfi 6384 unsnfidcex 6385 unsnfidcel 6386 finnum 6452 |
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