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

Theorem inab 3765
 Description: Intersection of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
inab

Proof of Theorem inab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sban 2140 . . 3
2 df-clab 2443 . . 3
3 df-clab 2443 . . . 4
4 df-clab 2443 . . . 4
53, 4anbi12i 697 . . 3
61, 2, 53bitr4ri 278 . 2
76ineqri 3691 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  i^icin 3474 This theorem is referenced by:  inrab  3769  inrab2  3770  dfrab3  3772  orduniss2  6668  ssenen  7711  hashf1lem2  12505  ballotlem2  28427  dfiota3  29573  ptrest  30048  diophin  30706  bj-inrab  34495 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-v 3111  df-in 3482
 Copyright terms: Public domain W3C validator