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Mirrors > Home > ILE Home > Th. List > rdgisucinc | Unicode version |
Description: Value of the recursive
definition generator at a successor.
This can be thought of as a generalization of oasuc 6423 and omsuc 6431. (Contributed by Jim Kingdon, 29-Aug-2019.) |
Ref | Expression |
---|---|
rdgisuc1.1 | |
rdgisuc1.2 | |
rdgisuc1.3 | |
rdgisucinc.inc |
Ref | Expression |
---|---|
rdgisucinc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rdgisuc1.1 | . . . 4 | |
2 | rdgisuc1.2 | . . . 4 | |
3 | rdgisuc1.3 | . . . 4 | |
4 | 1, 2, 3 | rdgisuc1 6343 | . . 3 |
5 | unass 3274 | . . 3 | |
6 | 4, 5 | eqtr4di 2215 | . 2 |
7 | rdgival 6341 | . . . 4 | |
8 | 1, 2, 3, 7 | syl3anc 1227 | . . 3 |
9 | 8 | uneq1d 3270 | . 2 |
10 | rdgexggg 6336 | . . . . 5 | |
11 | 1, 2, 3, 10 | syl3anc 1227 | . . . 4 |
12 | rdgisucinc.inc | . . . 4 | |
13 | id 19 | . . . . . 6 | |
14 | fveq2 5480 | . . . . . 6 | |
15 | 13, 14 | sseq12d 3168 | . . . . 5 |
16 | 15 | spcgv 2808 | . . . 4 |
17 | 11, 12, 16 | sylc 62 | . . 3 |
18 | ssequn1 3287 | . . 3 | |
19 | 17, 18 | sylib 121 | . 2 |
20 | 6, 9, 19 | 3eqtr2d 2203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wceq 1342 wcel 2135 cvv 2721 cun 3109 wss 3111 ciun 3860 con0 4335 csuc 4337 wfn 5177 cfv 5182 crdg 6328 |
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-in1 604 ax-in2 605 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-setind 4508 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 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-ne 2335 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-csb 3041 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-nul 3405 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-tr 4075 df-id 4265 df-iord 4338 df-on 4340 df-suc 4343 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 df-recs 6264 df-irdg 6329 |
This theorem is referenced by: frecrdg 6367 |
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