Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfrab3 Unicode version

Theorem dfrab3 3772
 Description: Alternate definition of restricted class abstraction. (Contributed by Mario Carneiro, 8-Sep-2013.)
Assertion
Ref Expression
dfrab3
Distinct variable group:   ,

Proof of Theorem dfrab3
StepHypRef Expression
1 df-rab 2816 . 2
2 inab 3765 . 2
3 abid2 2597 . . 3
43ineq1i 3695 . 2
51, 2, 43eqtr2i 2492 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  i^icin 3474 This theorem is referenced by:  dfrab2  3773  notrab  3774  dfrab3ss  3775  dfif3  3955  dffr3  5374  dfse2  5375  rabfi  7764  dfsup2  7922  ressmplbas2  18117  clsocv  21690  hasheuni  28091  tz6.26  29285  hashnzfz  31225 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-or 370  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-rab 2816  df-v 3111  df-in 3482
 Copyright terms: Public domain W3C validator