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Mirrors > Home > ILE Home > Th. List > setsvala | Unicode version |
Description: Value of the structure replacement function. (Contributed by Mario Carneiro, 1-Dec-2014.) (Revised by Jim Kingdon, 20-Jan-2023.) |
Ref | Expression |
---|---|
setsvala | sSet |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 966 | . . 3 | |
2 | opexg 4120 | . . . 4 | |
3 | 2 | 3adant1 984 | . . 3 |
4 | setsvalg 11916 | . . 3 sSet | |
5 | 1, 3, 4 | syl2anc 408 | . 2 sSet |
6 | dmsnopg 4980 | . . . . . 6 | |
7 | 6 | difeq2d 3164 | . . . . 5 |
8 | 7 | reseq2d 4789 | . . . 4 |
9 | 8 | uneq1d 3199 | . . 3 |
10 | 9 | 3ad2ant3 989 | . 2 |
11 | 5, 10 | eqtrd 2150 | 1 sSet |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 947 wceq 1316 wcel 1465 cvv 2660 cdif 3038 cun 3039 csn 3497 cop 3500 cdm 4509 cres 4511 (class class class)co 5742 sSet csts 11884 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-setind 4422 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-res 4521 df-iota 5058 df-fun 5095 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-sets 11893 |
This theorem is referenced by: setsex 11918 strsetsid 11919 fvsetsid 11920 setsabsd 11925 setscom 11926 setsslid 11936 |
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