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Mirrors > Home > ILE Home > Th. List > fliftel | Unicode version |
Description: Elementhood in the
relation ![]() |
Ref | Expression |
---|---|
flift.1 |
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flift.2 |
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flift.3 |
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Ref | Expression |
---|---|
fliftel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3756 |
. . . 4
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2 | flift.1 |
. . . . 5
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3 | 2 | eleq2i 2101 |
. . . 4
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4 | 1, 3 | bitri 173 |
. . 3
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5 | flift.2 |
. . . . . 6
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6 | flift.3 |
. . . . . 6
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7 | elex 2560 |
. . . . . . 7
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8 | elex 2560 |
. . . . . . 7
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9 | opexgOLD 3956 |
. . . . . . 7
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10 | 7, 8, 9 | syl2an 273 |
. . . . . 6
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11 | 5, 6, 10 | syl2anc 391 |
. . . . 5
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12 | 11 | ralrimiva 2386 |
. . . 4
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13 | eqid 2037 |
. . . . 5
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14 | 13 | elrnmptg 4529 |
. . . 4
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15 | 12, 14 | syl 14 |
. . 3
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16 | 4, 15 | syl5bb 181 |
. 2
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17 | opthg2 3967 |
. . . 4
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18 | 5, 6, 17 | syl2anc 391 |
. . 3
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19 | 18 | rexbidva 2317 |
. 2
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20 | 16, 19 | bitrd 177 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-mpt 3811 df-cnv 4296 df-dm 4298 df-rn 4299 |
This theorem is referenced by: fliftcnv 5378 fliftfun 5379 fliftf 5382 fliftval 5383 qliftel 6122 |
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