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Mirrors > Home > ILE Home > Th. List > frecabex | Unicode version |
Description: The class abstraction from df-frec 6350 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 4564 | . . . 4 | |
2 | simpr 109 | . . . . . . 7 | |
3 | 2 | abssi 3212 | . . . . . 6 |
4 | frecabex.sex | . . . . . . . 8 | |
5 | vex 2724 | . . . . . . . 8 | |
6 | fvexg 5499 | . . . . . . . 8 | |
7 | 4, 5, 6 | sylancl 410 | . . . . . . 7 |
8 | frecabex.fvex | . . . . . . 7 | |
9 | fveq2 5480 | . . . . . . . . 9 | |
10 | 9 | eleq1d 2233 | . . . . . . . 8 |
11 | 10 | spcgv 2808 | . . . . . . 7 |
12 | 7, 8, 11 | sylc 62 | . . . . . 6 |
13 | ssexg 4115 | . . . . . 6 | |
14 | 3, 12, 13 | sylancr 411 | . . . . 5 |
15 | 14 | ralrimivw 2538 | . . . 4 |
16 | abrexex2g 6080 | . . . 4 | |
17 | 1, 15, 16 | sylancr 411 | . . 3 |
18 | simpr 109 | . . . . 5 | |
19 | 18 | abssi 3212 | . . . 4 |
20 | frecabex.aex | . . . 4 | |
21 | ssexg 4115 | . . . 4 | |
22 | 19, 20, 21 | sylancr 411 | . . 3 |
23 | 17, 22 | jca 304 | . 2 |
24 | unexb 4414 | . . 3 | |
25 | unab 3384 | . . . 4 | |
26 | 25 | eleq1i 2230 | . . 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 698 wal 1340 wceq 1342 wcel 2135 cab 2150 wral 2442 wrex 2443 cvv 2721 cun 3109 wss 3111 c0 3404 csuc 4337 com 4561 cdm 4598 cfv 5182 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-coll 4091 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-iinf 4559 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-iom 4562 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 df-fv 5190 |
This theorem is referenced by: frectfr 6359 |
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