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Theorem unisng 3626
 Description: A set equals the union of its singleton. Theorem 8.2 of [Quine] p. 53. (Contributed by NM, 13-Aug-2002.)
Assertion
Ref Expression
unisng

Proof of Theorem unisng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3417 . . . 4
21unieqd 3620 . . 3
3 id 19 . . 3
42, 3eqeq12d 2096 . 2
5 vex 2605 . . 3
65unisn 3625 . 2
74, 6vtoclg 2659 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285   wcel 1434  csn 3406  cuni 3609 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-uni 3610 This theorem is referenced by:  dfnfc2  3627  unisucg  4177  unisn3  4206  opswapg  4837  funfvdm  5268  en2other2  6522
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