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

Theorem difdif 3629
 Description: Double class difference. Exercise 11 of [TakeutiZaring] p. 22. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
difdif

Proof of Theorem difdif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pm4.45im 562 . . 3
2 iman 424 . . . . 5
3 eldif 3485 . . . . 5
42, 3xchbinxr 311 . . . 4
54anbi2i 694 . . 3
61, 5bitr2i 250 . 2
76difeqri 3623 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  \cdif 3472 This theorem is referenced by:  dif0  3898  undifabs  3905 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-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-dif 3478
 Copyright terms: Public domain W3C validator