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Mirrors > Home > ILE Home > Th. List > ltexprlemelu | Unicode version |
Description: Element in upper cut of the constructed difference. Lemma for ltexpri 6803. (Contributed by Jim Kingdon, 21-Dec-2019.) |
Ref | Expression |
---|---|
ltexprlem.1 |
Ref | Expression |
---|---|
ltexprlemelu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 5540 | . . . . 5 | |
2 | 1 | eleq1d 2147 | . . . 4 |
3 | 2 | anbi2d 451 | . . 3 |
4 | 3 | exbidv 1746 | . 2 |
5 | ltexprlem.1 | . . . 4 | |
6 | 5 | fveq2i 5201 | . . 3 |
7 | nqex 6553 | . . . . 5 | |
8 | 7 | rabex 3922 | . . . 4 |
9 | 7 | rabex 3922 | . . . 4 |
10 | 8, 9 | op2nd 5794 | . . 3 |
11 | 6, 10 | eqtri 2101 | . 2 |
12 | 4, 11 | elrab2 2751 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 crab 2352 cop 3401 cfv 4922 (class class class)co 5532 c1st 5785 c2nd 5786 cnq 6470 cplq 6472 |
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-in1 576 ax-in2 577 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-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-coll 3893 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-iinf 4329 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-reu 2355 df-rab 2357 df-v 2603 df-sbc 2816 df-csb 2909 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-iun 3680 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-iom 4332 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 df-ov 5535 df-2nd 5788 df-qs 6135 df-ni 6494 df-nqqs 6538 |
This theorem is referenced by: ltexprlemm 6790 ltexprlemopu 6793 ltexprlemupu 6794 ltexprlemdisj 6796 ltexprlemloc 6797 ltexprlemfu 6801 ltexprlemru 6802 |
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