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

Theorem intexab 4610
 Description: The intersection of a nonempty class abstraction exists. (Contributed by NM, 21-Oct-2003.)
Assertion
Ref Expression
intexab

Proof of Theorem intexab
StepHypRef Expression
1 abn0 3804 . 2
2 intex 4608 . 2
31, 2bitr3i 251 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  E.wex 1612  e.wcel 1818  {cab 2442  =/=wne 2652   cvv 3109   c0 3784  |^|cint 4286 This theorem is referenced by:  intexrab  4611  tcmin  8193  cfval  8648  efgval  16735 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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573 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-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-int 4287
 Copyright terms: Public domain W3C validator