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Mirrors > Home > ILE Home > Th. List > rdgss | Unicode version |
Description: Subset and recursive definition generator. (Contributed by Jim Kingdon, 15-Jul-2019.) |
Ref | Expression |
---|---|
rdgss.1 | |
rdgss.2 | |
rdgss.3 | |
rdgss.4 | |
rdgss.5 |
Ref | Expression |
---|---|
rdgss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rdgss.5 | . . . 4 | |
2 | ssel 3091 | . . . . . 6 | |
3 | ssid 3117 | . . . . . . 7 | |
4 | fveq2 5421 | . . . . . . . . . 10 | |
5 | 4 | fveq2d 5425 | . . . . . . . . 9 |
6 | 5 | sseq2d 3127 | . . . . . . . 8 |
7 | 6 | rspcev 2789 | . . . . . . 7 |
8 | 3, 7 | mpan2 421 | . . . . . 6 |
9 | 2, 8 | syl6 33 | . . . . 5 |
10 | 9 | ralrimiv 2504 | . . . 4 |
11 | 1, 10 | syl 14 | . . 3 |
12 | iunss2 3858 | . . 3 | |
13 | unss2 3247 | . . 3 | |
14 | 11, 12, 13 | 3syl 17 | . 2 |
15 | rdgss.1 | . . 3 | |
16 | rdgss.2 | . . 3 | |
17 | rdgss.3 | . . 3 | |
18 | rdgival 6279 | . . 3 | |
19 | 15, 16, 17, 18 | syl3anc 1216 | . 2 |
20 | rdgss.4 | . . 3 | |
21 | rdgival 6279 | . . 3 | |
22 | 15, 16, 20, 21 | syl3anc 1216 | . 2 |
23 | 14, 19, 22 | 3sstr4d 3142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wral 2416 wrex 2417 cvv 2686 cun 3069 wss 3071 ciun 3813 con0 4285 wfn 5118 cfv 5123 crdg 6266 |
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 603 ax-in2 604 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 2121 ax-coll 4043 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-tr 4027 df-id 4215 df-iord 4288 df-on 4290 df-suc 4293 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-recs 6202 df-irdg 6267 |
This theorem is referenced by: oawordi 6365 |
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