MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eusn Unicode version

Theorem eusn 4106
Description: Two ways to express " is a singleton." (Contributed by NM, 30-Oct-2010.)
Assertion
Ref Expression
eusn
Distinct variable group:   ,

Proof of Theorem eusn
StepHypRef Expression
1 euabsn 4102 . 2
2 abid2 2597 . . . 4
32eqeq1i 2464 . . 3
43exbii 1667 . 2
51, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282  {cab 2442  {csn 4029
This theorem is referenced by:  reusv6OLD  4663  reusv7OLD  4664  funpartfv  29595  initoid  32611  termoid  32612  initoeu2lem1  32620  irinitoringc  32877
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-sn 4030
  Copyright terms: Public domain W3C validator