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Mirrors > Home > ILE Home > Th. List > acexmidlemv | Unicode version |
Description: Lemma for acexmid 5896.
This is acexmid 5896 with additional disjoint variable conditions,
most
notably between (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlemv.choice |
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Ref | Expression |
---|---|
acexmidlemv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onsucelsucexmidlem 4546 |
. . . 4
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2 | pp0ex 4207 |
. . . . 5
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3 | 2 | rabex 4162 |
. . . 4
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4 | prexg 4229 |
. . . 4
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5 | 1, 3, 4 | mp2an 426 |
. . 3
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6 | raleq 2686 |
. . . 4
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7 | 6 | exbidv 1836 |
. . 3
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8 | acexmidlemv.choice |
. . 3
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9 | 5, 7, 8 | vtocl 2806 |
. 2
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10 | eqeq1 2196 |
. . . . . 6
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11 | 10 | orbi1d 792 |
. . . . 5
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12 | 11 | cbvrabv 2751 |
. . . 4
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13 | eqeq1 2196 |
. . . . . 6
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14 | 13 | orbi1d 792 |
. . . . 5
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15 | 14 | cbvrabv 2751 |
. . . 4
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16 | eqid 2189 |
. . . 4
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17 | 12, 15, 16 | acexmidlem2 5894 |
. . 3
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18 | 17 | exlimiv 1609 |
. 2
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19 | 9, 18 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-uni 3825 df-tr 4117 df-iord 4384 df-on 4386 df-suc 4389 df-iota 5196 df-riota 5852 |
This theorem is referenced by: acexmid 5896 |
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