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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 6770 |
. . 3
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2 | 1 | eleq2i 2256 |
. 2
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3 | relen 6771 |
. . . . 5
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4 | 3 | brrelex1i 4687 |
. . . 4
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5 | 4 | rexlimivw 2603 |
. . 3
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6 | breq1 4021 |
. . . 4
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7 | 6 | rexbidv 2491 |
. . 3
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8 | 5, 7 | elab3 2904 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-rel 4651 df-en 6768 df-fin 6770 |
This theorem is referenced by: snfig 6841 fict 6897 fidceq 6898 nnfi 6901 enfi 6902 ssfilem 6904 dif1enen 6909 php5fin 6911 fisbth 6912 fin0 6914 fin0or 6915 diffitest 6916 findcard 6917 findcard2 6918 findcard2s 6919 diffisn 6922 infnfi 6924 fientri3 6944 unsnfi 6948 unsnfidcex 6949 unsnfidcel 6950 fiintim 6958 fidcenumlemim 6982 finnum 7213 hashcl 10796 hashen 10799 fihashdom 10818 hashun 10820 zfz1iso 10856 |
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