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Mirrors > Home > NFE 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 3747 | . . 3 | |
2 | 1 | unieqi 3901 | . 2 |
3 | unisn.1 | . . 3 | |
4 | 3, 3 | unipr 3905 | . 2 |
5 | unidm 3407 | . 2 | |
6 | 2, 4, 5 | 3eqtri 2377 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 wcel 1710 cvv 2859 cun 3207 csn 3737 cpr 3738 cuni 3891 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-uni 3892 |
This theorem is referenced by: unisng 3908 uniintsn 3963 pw1eqadj 4332 uniabio 4349 nnadjoin 4520 op1sta 5072 opswap 5074 op2nda 5076 funfv 5375 pw1fnval 5851 pw1fnf1o 5855 brtcfn 6246 |
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