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Mirrors > Home > ILE Home > Th. List > frecabex | Unicode version |
Description: The class abstraction from df-frec 6091 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 4374 |
. . . 4
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2 | simpr 108 |
. . . . . . 7
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3 | 2 | abssi 3082 |
. . . . . 6
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4 | frecabex.sex |
. . . . . . . 8
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5 | vex 2617 |
. . . . . . . 8
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6 | fvexg 5272 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 4, 5, 6 | sylancl 404 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | frecabex.fvex |
. . . . . . 7
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9 | fveq2 5256 |
. . . . . . . . 9
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10 | 9 | eleq1d 2153 |
. . . . . . . 8
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11 | 10 | spcgv 2698 |
. . . . . . 7
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12 | 7, 8, 11 | sylc 61 |
. . . . . 6
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13 | ssexg 3946 |
. . . . . 6
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14 | 3, 12, 13 | sylancr 405 |
. . . . 5
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15 | 14 | ralrimivw 2443 |
. . . 4
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16 | abrexex2g 5829 |
. . . 4
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17 | 1, 15, 16 | sylancr 405 |
. . 3
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18 | simpr 108 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | abssi 3082 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | frecabex.aex |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | ssexg 3946 |
. . . 4
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22 | 19, 20, 21 | sylancr 405 |
. . 3
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23 | 17, 22 | jca 300 |
. 2
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24 | unexb 4234 |
. . 3
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25 | unab 3252 |
. . . 4
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26 | 25 | eleq1i 2150 |
. . 3
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27 | 24, 26 | bitri 182 |
. 2
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28 | 23, 27 | sylib 120 |
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-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-13 1447 ax-14 1448 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-coll 3922 ax-sep 3925 ax-pow 3977 ax-pr 4003 ax-un 4227 ax-iinf 4369 |
This theorem depends on definitions: df-bi 115 df-3an 924 df-tru 1290 df-nf 1393 df-sb 1690 df-eu 1948 df-mo 1949 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ral 2360 df-rex 2361 df-reu 2362 df-rab 2364 df-v 2616 df-sbc 2829 df-csb 2922 df-un 2990 df-in 2992 df-ss 2999 df-pw 3411 df-sn 3431 df-pr 3432 df-op 3434 df-uni 3631 df-int 3666 df-iun 3709 df-br 3815 df-opab 3869 df-mpt 3870 df-id 4087 df-iom 4372 df-xp 4410 df-rel 4411 df-cnv 4412 df-co 4413 df-dm 4414 df-rn 4415 df-res 4416 df-ima 4417 df-iota 4937 df-fun 4974 df-fn 4975 df-f 4976 df-f1 4977 df-fo 4978 df-f1o 4979 df-fv 4980 |
This theorem is referenced by: frectfr 6100 |
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