Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfiota2 Unicode version

Theorem dfiota2 5557
 Description: Alternate definition for descriptions. Definition 8.18 in [Quine] p. 56. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
dfiota2
Distinct variable groups:   ,   ,

Proof of Theorem dfiota2
StepHypRef Expression
1 df-iota 5556 . 2
2 df-sn 4030 . . . . . 6
32eqeq2i 2475 . . . . 5
4 abbi 2588 . . . . 5
53, 4bitr4i 252 . . . 4
65abbii 2591 . . 3
76unieqi 4258 . 2
81, 7eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  {cab 2442  {csn 4029  U.cuni 4249  iotacio 5554 This theorem is referenced by:  nfiota1  5558  nfiotad  5559  cbviota  5561  sb8iota  5563  iotaval  5567  iotanul  5571  fv2  5866 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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-sn 4030  df-uni 4250  df-iota 5556
 Copyright terms: Public domain W3C validator