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Mirrors > Home > ILE Home > Th. List > un0 | Unicode version |
Description: The union of a class with the empty set is itself. Theorem 24 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
un0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3399 | . . . 4 | |
2 | 1 | biorfi 736 | . . 3 |
3 | 2 | bicomi 131 | . 2 |
4 | 3 | uneqri 3250 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 698 wceq 1335 wcel 2128 cun 3100 c0 3395 |
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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-un 3106 df-nul 3396 |
This theorem is referenced by: un00 3441 disjssun 3458 difun2 3474 difdifdirss 3479 disjpr2 3625 prprc1 3669 diftpsn3 3699 iununir 3934 suc0 4373 sucprc 4374 fvun1 5536 fmptpr 5661 fvunsng 5663 fvsnun1 5666 fvsnun2 5667 fsnunfv 5670 fsnunres 5671 rdg0 6336 omv2 6414 unsnfidcex 6866 unfidisj 6868 undifdc 6870 ssfirab 6880 dju0en 7151 djuassen 7154 fzsuc2 9987 fseq1p1m1 10002 hashunlem 10689 ennnfonelem1 12206 setsresg 12298 setsslid 12310 fmelpw1o 13452 exmid1stab 13643 |
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