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Mirrors > Home > ILE Home > Th. List > acexmidlemv | Unicode version |
Description: Lemma for acexmid 5766.
This is acexmid 5766 with additional distinct variable constraints, most notably between and . (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlemv.choice |
Ref | Expression |
---|---|
acexmidlemv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onsucelsucexmidlem 4439 | . . . 4 | |
2 | pp0ex 4108 | . . . . 5 | |
3 | 2 | rabex 4067 | . . . 4 |
4 | prexg 4128 | . . . 4 | |
5 | 1, 3, 4 | mp2an 422 | . . 3 |
6 | raleq 2624 | . . . 4 | |
7 | 6 | exbidv 1797 | . . 3 |
8 | acexmidlemv.choice | . . 3 | |
9 | 5, 7, 8 | vtocl 2735 | . 2 |
10 | eqeq1 2144 | . . . . . 6 | |
11 | 10 | orbi1d 780 | . . . . 5 |
12 | 11 | cbvrabv 2680 | . . . 4 |
13 | eqeq1 2144 | . . . . . 6 | |
14 | 13 | orbi1d 780 | . . . . 5 |
15 | 14 | cbvrabv 2680 | . . . 4 |
16 | eqid 2137 | . . . 4 | |
17 | 12, 15, 16 | acexmidlem2 5764 | . . 3 |
18 | 17 | exlimiv 1577 | . 2 |
19 | 9, 18 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wo 697 wceq 1331 wex 1468 wcel 1480 wral 2414 wrex 2415 wreu 2416 crab 2418 cvv 2681 c0 3358 csn 3522 cpr 3523 con0 4280 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-nul 4049 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-pw 3507 df-sn 3528 df-pr 3529 df-uni 3732 df-tr 4022 df-iord 4283 df-on 4285 df-suc 4288 df-iota 5083 df-riota 5723 |
This theorem is referenced by: acexmid 5766 |
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