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Mirrors > Home > ILE Home > Th. List > fliftel | Unicode version |
Description: Elementhood in the relation . (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
flift.1 | |
flift.2 | |
flift.3 |
Ref | Expression |
---|---|
fliftel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3765 | . . . 4 | |
2 | flift.1 | . . . . 5 | |
3 | 2 | eleq2i 2104 | . . . 4 |
4 | 1, 3 | bitri 173 | . . 3 |
5 | flift.2 | . . . . . 6 | |
6 | flift.3 | . . . . . 6 | |
7 | elex 2566 | . . . . . . 7 | |
8 | elex 2566 | . . . . . . 7 | |
9 | opexgOLD 3965 | . . . . . . 7 | |
10 | 7, 8, 9 | syl2an 273 | . . . . . 6 |
11 | 5, 6, 10 | syl2anc 391 | . . . . 5 |
12 | 11 | ralrimiva 2392 | . . . 4 |
13 | eqid 2040 | . . . . 5 | |
14 | 13 | elrnmptg 4586 | . . . 4 |
15 | 12, 14 | syl 14 | . . 3 |
16 | 4, 15 | syl5bb 181 | . 2 |
17 | opthg2 3976 | . . . 4 | |
18 | 5, 6, 17 | syl2anc 391 | . . 3 |
19 | 18 | rexbidva 2323 | . 2 |
20 | 16, 19 | bitrd 177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wral 2306 wrex 2307 cvv 2557 cop 3378 class class class wbr 3764 cmpt 3818 crn 4346 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-mpt 3820 df-cnv 4353 df-dm 4355 df-rn 4356 |
This theorem is referenced by: fliftcnv 5435 fliftfun 5436 fliftf 5439 fliftval 5440 qliftel 6186 |
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