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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 3222 |
. . . 4
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2 | 1 | biorfi 664 |
. . 3
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3 | 2 | bicomi 123 |
. 2
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4 | 3 | uneqri 3079 |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-dif 2914 df-un 2916 df-nul 3219 |
This theorem is referenced by: un00 3257 disjssun 3279 difun2 3296 difdifdirss 3301 disjpr2 3425 prprc1 3469 diftpsn3 3496 iununir 3729 suc0 4114 sucprc 4115 fvun1 5182 fmptpr 5298 fvunsng 5300 fvsnun1 5303 fvsnun2 5304 fsnunfv 5306 fsnunres 5307 rdg0 5914 omv2 5984 fzsuc2 8711 fseq1p1m1 8726 |
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