Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  unisng Unicode version

Theorem unisng 3597
 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 3386 . . . 4
21unieqd 3591 . . 3
3 id 19 . . 3
42, 3eqeq12d 2054 . 2
5 vex 2560 . . 3
65unisn 3596 . 2
74, 6vtoclg 2613 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  csn 3375  cuni 3580 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581 This theorem is referenced by:  dfnfc2  3598  unisucg  4151  unisn3  4180  opswapg  4807  funfvdm  5236
 Copyright terms: Public domain W3C validator