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Mirrors > Home > ILE Home > Th. List > frecabex | Unicode version |
Description: The class abstraction from df-frec 6239 exists. This is a lemma for other finite recursion proofs. (Contributed by Jim Kingdon, 13-May-2020.) |
Ref | Expression |
---|---|
frecabex.sex |
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frecabex.fvex |
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frecabex.aex |
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Ref | Expression |
---|---|
frecabex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omex 4465 |
. . . 4
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2 | simpr 109 |
. . . . . . 7
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3 | 2 | abssi 3136 |
. . . . . 6
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4 | frecabex.sex |
. . . . . . . 8
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5 | vex 2658 |
. . . . . . . 8
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6 | fvexg 5392 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 4, 5, 6 | sylancl 407 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | frecabex.fvex |
. . . . . . 7
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9 | fveq2 5373 |
. . . . . . . . 9
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10 | 9 | eleq1d 2181 |
. . . . . . . 8
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11 | 10 | spcgv 2742 |
. . . . . . 7
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12 | 7, 8, 11 | sylc 62 |
. . . . . 6
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13 | ssexg 4025 |
. . . . . 6
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14 | 3, 12, 13 | sylancr 408 |
. . . . 5
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15 | 14 | ralrimivw 2478 |
. . . 4
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16 | abrexex2g 5969 |
. . . 4
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17 | 1, 15, 16 | sylancr 408 |
. . 3
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18 | simpr 109 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | abssi 3136 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | frecabex.aex |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | ssexg 4025 |
. . . 4
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22 | 19, 20, 21 | sylancr 408 |
. . 3
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23 | 17, 22 | jca 302 |
. 2
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24 | unexb 4321 |
. . 3
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25 | unab 3307 |
. . . 4
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26 | 25 | eleq1i 2178 |
. . 3
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27 | 24, 26 | bitri 183 |
. 2
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28 | 23, 27 | sylib 121 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-coll 4001 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-iinf 4460 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-reu 2395 df-rab 2397 df-v 2657 df-sbc 2877 df-csb 2970 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-int 3736 df-iun 3779 df-br 3894 df-opab 3948 df-mpt 3949 df-id 4173 df-iom 4463 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-rn 4508 df-res 4509 df-ima 4510 df-iota 5044 df-fun 5081 df-fn 5082 df-f 5083 df-f1 5084 df-fo 5085 df-f1o 5086 df-fv 5087 |
This theorem is referenced by: frectfr 6248 |
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