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Mirrors > Home > ILE Home > Th. List > frecabex | Unicode version |
Description: The class abstraction from df-frec 6281 exists. This is a lemma for other finite recursion proofs. (Contributed by Jim Kingdon, 13-May-2020.) |
Ref | Expression |
---|---|
frecabex.sex | |
frecabex.fvex | |
frecabex.aex |
Ref | Expression |
---|---|
frecabex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omex 4502 | . . . 4 | |
2 | simpr 109 | . . . . . . 7 | |
3 | 2 | abssi 3167 | . . . . . 6 |
4 | frecabex.sex | . . . . . . . 8 | |
5 | vex 2684 | . . . . . . . 8 | |
6 | fvexg 5433 | . . . . . . . 8 | |
7 | 4, 5, 6 | sylancl 409 | . . . . . . 7 |
8 | frecabex.fvex | . . . . . . 7 | |
9 | fveq2 5414 | . . . . . . . . 9 | |
10 | 9 | eleq1d 2206 | . . . . . . . 8 |
11 | 10 | spcgv 2768 | . . . . . . 7 |
12 | 7, 8, 11 | sylc 62 | . . . . . 6 |
13 | ssexg 4062 | . . . . . 6 | |
14 | 3, 12, 13 | sylancr 410 | . . . . 5 |
15 | 14 | ralrimivw 2504 | . . . 4 |
16 | abrexex2g 6011 | . . . 4 | |
17 | 1, 15, 16 | sylancr 410 | . . 3 |
18 | simpr 109 | . . . . 5 | |
19 | 18 | abssi 3167 | . . . 4 |
20 | frecabex.aex | . . . 4 | |
21 | ssexg 4062 | . . . 4 | |
22 | 19, 20, 21 | sylancr 410 | . . 3 |
23 | 17, 22 | jca 304 | . 2 |
24 | unexb 4358 | . . 3 | |
25 | unab 3338 | . . . 4 | |
26 | 25 | eleq1i 2203 | . . 3 |
27 | 24, 26 | bitri 183 | . 2 |
28 | 23, 27 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 697 wal 1329 wceq 1331 wcel 1480 cab 2123 wral 2414 wrex 2415 cvv 2681 cun 3064 wss 3066 c0 3358 csuc 4282 com 4499 cdm 4534 cfv 5118 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-coll 4038 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-iinf 4497 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-int 3767 df-iun 3810 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-iom 4500 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 df-fv 5126 |
This theorem is referenced by: frectfr 6290 |
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