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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 3228 |
. . . 4
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2 | 1 | biorfi 665 |
. . 3
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3 | 2 | bicomi 123 |
. 2
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4 | 3 | uneqri 3085 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-un 2922 df-nul 3225 |
This theorem is referenced by: un00 3263 disjssun 3285 difun2 3302 difdifdirss 3307 disjpr2 3434 prprc1 3478 diftpsn3 3505 iununir 3738 suc0 4148 sucprc 4149 fvun1 5239 fmptpr 5355 fvunsng 5357 fvsnun1 5360 fvsnun2 5361 fsnunfv 5363 fsnunres 5364 rdg0 5974 omv2 6045 fzsuc2 8941 fseq1p1m1 8956 |
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