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Mirrors > Home > ILE Home > Th. List > reg3exmid | Unicode version |
Description: If any inhabited set
satisfying df-wetr 4161 for ![]() |
Ref | Expression |
---|---|
reg3exmid.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
reg3exmid |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2088 |
. . 3
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2 | 1 | regexmidlemm 4348 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | 1 | reg3exmidlemwe 4394 |
. . 3
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4 | pp0ex 4024 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | rabex 3983 |
. . . 4
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6 | weeq2 4184 |
. . . . . 6
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7 | eleq2 2151 |
. . . . . . 7
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8 | 7 | exbidv 1753 |
. . . . . 6
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9 | 6, 8 | anbi12d 457 |
. . . . 5
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10 | raleq 2562 |
. . . . . 6
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11 | 10 | rexeqbi1dv 2571 |
. . . . 5
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12 | 9, 11 | imbi12d 232 |
. . . 4
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13 | reg3exmid.1 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 5, 12, 13 | vtocl 2673 |
. . 3
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15 | 3, 14 | mpan 415 |
. 2
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16 | 1 | reg2exmidlema 4350 |
. 2
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17 | 2, 15, 16 | mp2b 8 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-nul 3965 ax-pow 4009 ax-pr 4036 ax-setind 4353 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-rex 2365 df-rab 2368 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 df-opab 3900 df-eprel 4116 df-frfor 4158 df-frind 4159 df-wetr 4161 |
This theorem is referenced by: (None) |
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