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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3441 |
. . . 4
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2 | 1 | biorfi 747 |
. . 3
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3 | 2 | bicomi 132 |
. 2
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4 | 3 | uneqri 3292 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-dif 3146 df-un 3148 df-nul 3438 |
This theorem is referenced by: un00 3484 disjssun 3501 difun2 3517 difdifdirss 3522 disjpr2 3671 prprc1 3715 diftpsn3 3748 iununir 3985 exmid1stab 4226 suc0 4429 sucprc 4430 fvun1 5602 fmptpr 5728 fvunsng 5730 fvsnun1 5733 fvsnun2 5734 fsnunfv 5737 fsnunres 5738 rdg0 6411 omv2 6489 unsnfidcex 6947 unfidisj 6949 undifdc 6951 ssfirab 6961 dju0en 7242 djuassen 7245 fzsuc2 10108 fseq1p1m1 10123 hashunlem 10815 ennnfonelem1 12457 setsresg 12549 setsslid 12562 fmelpw1o 15011 |
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