ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  abid2 Unicode version

Theorem abid2 2208
Description: A simplification of class abstraction. Theorem 5.2 of [Quine] p. 35. (Contributed by NM, 26-Dec-1993.)
Assertion
Ref Expression
abid2  |-  { x  |  x  e.  A }  =  A
Distinct variable group:    x, A

Proof of Theorem abid2
StepHypRef Expression
1 biid 169 . . 3  |-  ( x  e.  A  <->  x  e.  A )
21abbi2i 2202 . 2  |-  A  =  { x  |  x  e.  A }
32eqcomi 2092 1  |-  { x  |  x  e.  A }  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1289    e. wcel 1438   {cab 2074
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-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084
This theorem is referenced by:  csbid  2938  abss  3088  ssab  3089  abssi  3094  notab  3267  inrab2  3270  dfrab2  3272  dfrab3  3273  notrab  3274  eusn  3511  dfopg  3615  iunid  3780  csbexga  3959  imai  4775  dffv4g  5286  frec0g  6144  euen1b  6500
  Copyright terms: Public domain W3C validator