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

Theorem intss 4307
 Description: Intersection of subclasses. (Contributed by NM, 14-Oct-1999.) (Proof shortened by OpenAI, 25-Mar-2020.)
Assertion
Ref Expression
intss

Proof of Theorem intss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssralv 3563 . . 3
21ss2abdv 3572 . 2
3 dfint2 4288 . 2
4 dfint2 4288 . 2
52, 3, 43sstr4g 3544 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  {cab 2442  A.wral 2807  C_wss 3475  |^|cint 4286 This theorem is referenced by:  uniintsn  4324  intabs  4613  fiss  7904  tc2  8194  tcss  8196  tcel  8197  rankval4  8306  cfub  8650  cflm  8651  cflecard  8654  fin23lem26  8726  mrcss  15013  lspss  17630  lbsextlem3  17806  aspss  17981  clsss  19555  1stcfb  19946  ufinffr  20430  spanss  26266  ss2mcls  28928  pclssN  35618  dochspss  37105 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-ral 2812  df-in 3482  df-ss 3489  df-int 4287
 Copyright terms: Public domain W3C validator