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

Theorem disjr 3661
 Description: Two ways of saying that two classes are disjoint. (Contributed by Jeff Madsen, 19-Jun-2011.)
Assertion
Ref Expression
disjr
Distinct variable groups:   ,   ,

Proof of Theorem disjr
StepHypRef Expression
1 incom 3525 . . 3
21eqeq1i 2442 . 2
3 disj 3660 . 2
42, 3bitri 241 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wceq 1652   wcel 1725  wral 2697   cin 3311  c0 3620 This theorem is referenced by:  zfreg2  7556  kqdisj  17756  iccntr  18844  stoweidlem57  27773 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-dif 3315  df-in 3319  df-nul 3621
 Copyright terms: Public domain W3C validator