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Mirrors > Home > ILE Home > Th. List > acexmidlemab | Unicode version |
Description: Lemma for acexmid 5781. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a |
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acexmidlem.b |
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acexmidlem.c |
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Ref | Expression |
---|---|
acexmidlemab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3372 |
. . . 4
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2 | 0ex 4063 |
. . . . . 6
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3 | 2 | snid 3563 |
. . . . 5
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4 | eleq2 2204 |
. . . . 5
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5 | 3, 4 | mpbiri 167 |
. . . 4
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6 | 1, 5 | mto 652 |
. . 3
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7 | acexmidlem.a |
. . . . . . . . . 10
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8 | acexmidlem.b |
. . . . . . . . . 10
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9 | acexmidlem.c |
. . . . . . . . . 10
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10 | 7, 8, 9 | acexmidlemph 5775 |
. . . . . . . . 9
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11 | id 19 |
. . . . . . . . . 10
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12 | eleq1 2203 |
. . . . . . . . . . . 12
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13 | 12 | anbi1d 461 |
. . . . . . . . . . 11
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14 | 13 | rexbidv 2439 |
. . . . . . . . . 10
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15 | 11, 14 | riotaeqbidv 5741 |
. . . . . . . . 9
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16 | 10, 15 | syl 14 |
. . . . . . . 8
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17 | 16 | eqeq1d 2149 |
. . . . . . 7
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18 | 17 | biimpa 294 |
. . . . . 6
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19 | 18 | adantrr 471 |
. . . . 5
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20 | simprr 522 |
. . . . 5
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21 | 19, 20 | eqtr3d 2175 |
. . . 4
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22 | 21 | ex 114 |
. . 3
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23 | 6, 22 | mtoi 654 |
. 2
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24 | 23 | con2i 617 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-nul 4062 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-nul 3369 df-sn 3538 df-uni 3745 df-iota 5096 df-riota 5738 |
This theorem is referenced by: acexmidlem1 5778 |
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