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Mirrors > Home > ILE Home > Th. List > isfi | Unicode version |
Description: Express "![]() ![]() |
Ref | Expression |
---|---|
isfi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fin 6737 |
. . 3
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2 | 1 | eleq2i 2244 |
. 2
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3 | relen 6738 |
. . . . 5
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4 | 3 | brrelex1i 4666 |
. . . 4
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5 | 4 | rexlimivw 2590 |
. . 3
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6 | breq1 4003 |
. . . 4
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7 | 6 | rexbidv 2478 |
. . 3
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8 | 5, 7 | elab3 2889 |
. 2
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9 | 2, 8 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-xp 4629 df-rel 4630 df-en 6735 df-fin 6737 |
This theorem is referenced by: snfig 6808 fict 6862 fidceq 6863 nnfi 6866 enfi 6867 ssfilem 6869 dif1enen 6874 php5fin 6876 fisbth 6877 fin0 6879 fin0or 6880 diffitest 6881 findcard 6882 findcard2 6883 findcard2s 6884 diffisn 6887 infnfi 6889 fientri3 6908 unsnfi 6912 unsnfidcex 6913 unsnfidcel 6914 fiintim 6922 fidcenumlemim 6945 finnum 7176 hashcl 10745 hashen 10748 fihashdom 10767 hashun 10769 zfz1iso 10805 |
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