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Mirrors > Home > ILE Home > Th. List > unisng | Unicode version |
Description: A set equals the union of its singleton. Theorem 8.2 of [Quine] p. 53. (Contributed by NM, 13-Aug-2002.) |
Ref | Expression |
---|---|
unisng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3584 | . . . 4 | |
2 | 1 | unieqd 3797 | . . 3 |
3 | id 19 | . . 3 | |
4 | 2, 3 | eqeq12d 2179 | . 2 |
5 | vex 2727 | . . 3 | |
6 | 5 | unisn 3802 | . 2 |
7 | 4, 6 | vtoclg 2784 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 csn 3573 cuni 3786 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2726 df-un 3118 df-sn 3579 df-pr 3580 df-uni 3787 |
This theorem is referenced by: dfnfc2 3804 unisucg 4389 unisn3 4420 opswapg 5087 funfvdm 5546 en2other2 7146 |
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