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Mirrors > Home > ILE Home > Th. List > acexmidlemv | Unicode version |
Description: Lemma for acexmid 5850.
This is acexmid 5850 with additional disjoint variable conditions, most notably between and . (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlemv.choice |
Ref | Expression |
---|---|
acexmidlemv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onsucelsucexmidlem 4511 | . . . 4 | |
2 | pp0ex 4173 | . . . . 5 | |
3 | 2 | rabex 4131 | . . . 4 |
4 | prexg 4194 | . . . 4 | |
5 | 1, 3, 4 | mp2an 424 | . . 3 |
6 | raleq 2665 | . . . 4 | |
7 | 6 | exbidv 1818 | . . 3 |
8 | acexmidlemv.choice | . . 3 | |
9 | 5, 7, 8 | vtocl 2784 | . 2 |
10 | eqeq1 2177 | . . . . . 6 | |
11 | 10 | orbi1d 786 | . . . . 5 |
12 | 11 | cbvrabv 2729 | . . . 4 |
13 | eqeq1 2177 | . . . . . 6 | |
14 | 13 | orbi1d 786 | . . . . 5 |
15 | 14 | cbvrabv 2729 | . . . 4 |
16 | eqid 2170 | . . . 4 | |
17 | 12, 15, 16 | acexmidlem2 5848 | . . 3 |
18 | 17 | exlimiv 1591 | . 2 |
19 | 9, 18 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wo 703 wceq 1348 wex 1485 wcel 2141 wral 2448 wrex 2449 wreu 2450 crab 2452 cvv 2730 c0 3414 csn 3581 cpr 3582 con0 4346 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-nul 4113 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3or 974 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-reu 2455 df-rab 2457 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 df-uni 3795 df-tr 4086 df-iord 4349 df-on 4351 df-suc 4354 df-iota 5158 df-riota 5807 |
This theorem is referenced by: acexmid 5850 |
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