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Mirrors > Home > ILE Home > Th. List > unisn | Unicode version |
Description: A set equals the union of its singleton. Theorem 8.2 of [Quine] p. 53. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
unisn.1 |
Ref | Expression |
---|---|
unisn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3574 | . . 3 | |
2 | 1 | unieqi 3782 | . 2 |
3 | unisn.1 | . . 3 | |
4 | 3, 3 | unipr 3786 | . 2 |
5 | unidm 3250 | . 2 | |
6 | 2, 4, 5 | 3eqtri 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wcel 2128 cvv 2712 cun 3100 csn 3560 cpr 3561 cuni 3772 |
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-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-rex 2441 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-uni 3773 |
This theorem is referenced by: unisng 3789 uniintsnr 3843 unisuc 4373 op1sta 5067 op2nda 5070 elxp4 5073 uniabio 5145 iotass 5152 en1bg 6745 |
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