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Mirrors > Home > ILE Home > Th. List > tfrlemibex | Unicode version |
Description: The set exists. Lemma for tfrlemi1 6197. (Contributed by Jim Kingdon, 17-Mar-2019.) (Proof shortened by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
tfrlemisucfn.1 | |
tfrlemisucfn.2 | |
tfrlemi1.3 | |
tfrlemi1.4 | |
tfrlemi1.5 |
Ref | Expression |
---|---|
tfrlemibex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlemisucfn.1 | . . . 4 | |
2 | tfrlemisucfn.2 | . . . 4 | |
3 | tfrlemi1.3 | . . . 4 | |
4 | tfrlemi1.4 | . . . 4 | |
5 | tfrlemi1.5 | . . . 4 | |
6 | 1, 2, 3, 4, 5 | tfrlemibfn 6193 | . . 3 |
7 | vex 2663 | . . 3 | |
8 | fnex 5610 | . . 3 | |
9 | 6, 7, 8 | sylancl 409 | . 2 |
10 | uniexb 4364 | . 2 | |
11 | 9, 10 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wal 1314 wceq 1316 wex 1453 wcel 1465 cab 2103 wral 2393 wrex 2394 cvv 2660 cun 3039 csn 3497 cop 3500 cuni 3706 con0 4255 cres 4511 wfun 5087 wfn 5088 cfv 5093 |
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-coll 4013 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-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-tr 3997 df-id 4185 df-iord 4258 df-on 4260 df-suc 4263 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-recs 6170 |
This theorem is referenced by: tfrlemiex 6196 |
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