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

Theorem unrab 3768
 Description: Union of two restricted class abstractions. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
unrab

Proof of Theorem unrab
StepHypRef Expression
1 df-rab 2816 . . 3
2 df-rab 2816 . . 3
31, 2uneq12i 3655 . 2
4 df-rab 2816 . . 3
5 unab 3764 . . . 4
6 andi 867 . . . . 5
76abbii 2591 . . . 4
85, 7eqtr4i 2489 . . 3
94, 8eqtr4i 2489 . 2
103, 9eqtr4i 2489 1
 Colors of variables: wff setvar class Syntax hints:  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  u.cun 3473 This theorem is referenced by:  rabxm  3808  kmlem3  8553  hashbclem  12501  phiprmpw  14306  efgsfo  16757  dsmmacl  18772  rrxmvallem  21831  mumul  23455  ppiub  23479  lgsquadlem2  23630  numclwwlk3lem  25108  hasheuni  28091  measvuni  28185  aean  28216  subfacp1lem6  28629  lineunray  29797  cnambfre  30063  itg2addnclem2  30067  iblabsnclem  30078  orrabdioph  30715  undisjrab  31186  mndpsuppss  32964 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-un 3480
 Copyright terms: Public domain W3C validator