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Mirrors > Home > ILE Home > Th. List > tfrlemibex | Unicode version |
Description: The set exists. Lemma for tfrlemi1 6282. (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 6278 | . . 3 |
7 | vex 2715 | . . 3 | |
8 | fnex 5692 | . . 3 | |
9 | 6, 7, 8 | sylancl 410 | . 2 |
10 | uniexb 4436 | . 2 | |
11 | 9, 10 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wal 1333 wceq 1335 wex 1472 wcel 2128 cab 2143 wral 2435 wrex 2436 cvv 2712 cun 3100 csn 3561 cop 3564 cuni 3774 con0 4326 cres 4591 wfun 5167 wfn 5168 cfv 5173 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-coll 4082 ax-sep 4085 ax-pow 4138 ax-pr 4172 ax-un 4396 ax-setind 4499 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-iun 3853 df-br 3968 df-opab 4029 df-mpt 4030 df-tr 4066 df-id 4256 df-iord 4329 df-on 4331 df-suc 4334 df-xp 4595 df-rel 4596 df-cnv 4597 df-co 4598 df-dm 4599 df-rn 4600 df-res 4601 df-ima 4602 df-iota 5138 df-fun 5175 df-fn 5176 df-f 5177 df-f1 5178 df-fo 5179 df-f1o 5180 df-fv 5181 df-recs 6255 |
This theorem is referenced by: tfrlemiex 6281 |
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